Question:
If Jesus (Y'shua) was Hebrew and all of the original apostles were Hebrews, it seems to make sense that they would have spoken, talked to one another, and written to one another in Hebrew.

Answer:
Let me look first at exactly what you are indicating with this comment.  There are several problematic assumptions in your comment.

First, how would one of their ethnic names tell you what language they spoke?  Jesus (Iesous, Yoshua, etc) was a Galilean, does that mean he spoke Galilean?  No, I don't know of any language by that name.  The Romans spoke Roman, right?  No, their language was called Latin, and Latin was the native language of other tribes also.

What is the primary language in Canada, Canadian?  I don't think so, the primary language in Canada is called English, and there are other languages spoken also, like in most countries.

And, I guess if you live in America, you speak American, right?  But maybe you live in the United States, so you must speak Unitedstatesian, correct?

There is no direct or necessary connection between an ethnic name and a particular name of a language.  There is similarly no necessary relationship between a particular genetic or cultural stream of humans and any particular stream of language usage.

What about Americans who call their language English?  What about Scots who call their language Gaelic?  Texans who speak Spanish?  Bretons whose native language is French, not Breton?  What about American Poles whose native language is English?  In New York City once, my cab driver, speaking Yiddish with a toll taker at a bridge, told me he was speaking "Jewish."

Second, your comment assumes that the form of speech we know by the name "Hebrew" was still being spoken as a common language at that time.  That is, in fact, one of the factors in contention in this topic!

You additionally assume Jesus was called, or called himself, "Hebrew."  What do you mean by this designation?  What does this term mean in the 1st century?  Speech forms are called by various names.  And the name of an ethnic group may only incidentally be related to a historical name for some form of speech.  Do you in fact, have any record, that Jesus called himself a Hebrew?

Because someone calls themselves (or are called by others) by a certain ethnic name, it does not follow that the language they speak must be called by that same name!  Or that some form of speech called by that name would still be spoken by a particular group of people who might be referred to by that name.  Did people who called themselves "Hebrew" speak a language called Hebrew, or Aramaic as the sources of the period indicate?

Where in the New Testament writings is this term "Hebrew" applied to Jesus?  Does Jesus ever tell us what ethnicity he is, or refer by name to the language he speaks?

Evidence
First of all, I have not seen any biblical or historical evidence indicating that Jesus claimed to be "Hebrew."  The references in the Gospels are unclear on what ethnic term he used for himself.  A common term for the people of Judea and the Jewish regions was "Jew," which is, of course, why the adjective form "Jewish" is used!  The normal term used at that time was "Jew."

The English term comes from the name of the province Yudea (formerly Yehuda of the Assyrian Empire and then the Chaldean).  The name derives from the tribe of Yudah or Yahuda (Judah).  The returnees from the Babylonian Exile who reestablished Jerusalem and the Temple were Judeans (and their descendants) who had been taken away by the Chaldean Nebuchadnezzar of the neo-Babylonian Empire.  The people of the province of Judea were Judeans, which through phonetic changes over 2000 years and through several languages, into the new language of English comes out as "Jew."

Thus the common ethnic term of reference we see at that time is "Jew" and "Jewish."  "Hebrew" occurs on occasion.  We do see a distinction in the Gospels between Jew (from Judea) and Galilean (from Galilee).  And the Gospels are very clear that Jesus was a Galilean.

Galilee vs Judea
The distinction between Galilean and Judean plays very large in the attitude of the Judean leaders and their view of the Galilean problem.  As were much of the Galilean population, Jesus and his family are portrayed as of Jewish descent, and the genealogies report Jesus as a descendant of King David (though the two genealogies in Matthew and Luke differ, and both show the lineage through Joseph).

Historical sources from the period likewise are very clear on this.  For example, the extensive writings by Josephus, a Jewish priest, military leader (first for the Judean rebellion, then for the Romans) and chronicler of Jewish and Roman history.

Like any word or name, this word "Hebrew" has different references over the centuries and millennia when it was used.  First of all, we have no evidence that the people commonly call themselves Hebrews.  There are a couple of references in the New Testament.

Instances I think of are referring to historical ethnic origins.  For instance, Paul, in clarifying his devotion as a Jew, says he is "of the stock of Israel" and "a Hebrew of the Hebrews" (Phil 3:5), meaning both his parents were of Hebrew historical and genetic heritage.  There is no indication in the New Testament that anyone spoke what we know as the Hebrew language.

Abraham
Because of the historical and cultural events of the previous 500 years in Palestine, we find that at the time of Jesus even descendants of other tribes besides Judah identified themselves with the Jews and their worship.  Note that the apostle Paul identifies himself as of the tribe of Benjamin.  The term he commonly uses to identify himself is Jew or "descendant of Abraham."  Even though a descendant of Benjamin, he called himself a Jew (descendant of Judah).  For instance, in Acts 21:39 and Acts 22:3, Paul says "I am a Jew of Tarsus."

Likewise, Luke identifies the prophetess Anna as a member of the tribe of Asher (Luke 2:36), one of the ten northern tribes from whom a large portion of their population was taken away by Assyria and settled in various locations to diminish the political-ethnic strength of Samaria-Israel.  These other descendants of the ancient Hebrew tribes in Palestine apparently likewise did not call themselves Hebrew.

A Name
The term Hebrew was still used some in the first century before and after Christ.  But the word was used more as a historical identification.  The people were mainly known by the tribal history or region they lived in.  Thus Galileans were different from Judeans.  I discuss these factors at length and quote several other authorities.

Languages themselves change over time.  A people can shift into another language stream, which seems to be what happened to the Jews, the descendants of the Hebrew ethnic stream.  A Jewish ethnic stream developed after the Exile.

The examples of the Prussian people illustrates one process that can occur in ethnic change.  The "Prussian" people of what is now Germany are not even the same people as the original "Prussians," who were not Germanic but a group of the much earlier Baltic people.  Names change, peoples change, times change, languages change.

Separate Division
Jesus was a Galilean.  The various Palestinian domains of Galilee and Judea were not even in the same political division of the Roman Empire.  Herod ruled Galilee and Perea across the Jordan River, while Pilate was made the direct Roman governor of the province of Judea.  I address this in several interlinked articles.

We do know Aramaic was commonly used in the synagogues due to the Targum (translations), which were readings of portions of the Hebrew scriptures.  It appears these were at least one basis of early translations of the Hebrew Scriptures (which are somewhat similar to the Christian "Old Testament") into the Aramaic languages that existed at the time.

It seems well established that the Jews in the Empire spoke Greek as a native language.  (They were called Hellenists or Hellenistic Jews, even in the New Testament writings.) The Greek context and style of the letters of Paul have been probed and analyzed in detail, confirming that the whole of Paul's letters reflect the literary forms of Greek rhetoric and writing style and the oral patterns of classical Greek drama and philosophy.

A correspondent referred me to Michael Rood.  I have referenced the website and looked over his claims that the whole of New Testament writings were written in Hebrew.  I am not impressed.  His arguments are ideological, and ignore a considerable body of information about history, culture and language.  He and others with similar views use sophistic logic that defies both common sense and the collected body of relevant information, as well as both ancient sources and modern analysis and insights.

Evidence Against Hebrew
One of the common evidences against Hebrew being a commonly spoken language is the name forms that are given in the New Testament writings, especially the Gospels.  Many persons are referred to by the name Bar {Father's Name}.  This is the Aramaic phrase.

For instance, Jesus addresses Simon Peter as Simon Bar Jona (Aramaic for Simon son of Jonah), not the Hebrew form Simon Ben Jona (Matt 16:17).  In Acts 13:6 we read of a Jewish false prophet in Paphos named Bar Jesus.  Another example was Bar Timaeus (Mark 10:46).

The latter, incidentally, also indicates how common Greek names were in Galilee.  Timaeus is one of the characters in one of Plato's dialogues.  The name is common, and is a Greek word meaning cashier, accountant or money manager.  Even today, the Greek word for a checkout till in a store is a form of this word, timeo.

Even in the 400s BCE, Jews as far away as Upper Egypt were using Aramaic, not Hebrew as a major language, though written texts also appear in Hebrew from that period.  This Jewish colony of Elephantine is associated with the period of the Exile, likely the group Jeremiah writes about, with whom he may have spent some time.  It is likely, however, that there was already a settlement of Jews there, to whom these refugees fled.*  Dr J A Emerton provides some helpful information regarding this.  He comments on the substantial Jewish community well established in the time before the return of the Judeans from Babylon:

"A Jewish colony at Elephantine (Yeb) in Upper Egypt has left many Aramaic papyri from the fifth century BCE (including letters about the rebuilding of a Jewish temple there and about the Passover" [J A Emerton, "Aramaic," Oxford Companion to the Bible (Oxford/NY: Oxford University Press, 1993), p 45].

This indicates that even the Jews who had fled Judea under the Chaldeans were already well established in the Aramaic language, using it in their own records in preference to Hebrew.  The fact that the language used in their letters are Aramaic is significant as an indicator of their native or primary tongue.

Dr Emerton further comments on Jesus specifically:

"As a Galilean, Jesus spoke Aramaic and on the cross he quoted Psalm 22:1 in Aramaic, not in the Hebrew original, but he probably also spoke Hebrew.  When Rabban Gamaliel wrote to Jews in Galilee – probably in the late first century CE – he wrote in Aramaic, according to the Talmud (Sanh. 11B) [J A Emerton, "Aramaic," Oxford Companion to the Bible (Oxford/NY: Oxford University Press, 1993), p 46]."

Greek
There are many indications that Greek had become a common language of all the peoples of Palestine, including the Jews in both Judea and Galilee.  One clear sign that Greek was the dominant language is that it is not common to find Hebrew or even Aramaic funerary inscriptions on graves or ossuaries.  Even in Judea, archaeologists have found that 2/3 of these are in the Greek language, in the period from 300 BC to 500 AD.

Note that there is a set of interlinked and cross-referenced articles on this site discussing different aspects of the settings and factors related to the writings of the documents found in the New Testament.  All the articles link to various sources.  Also some comments may refer to concepts developed in the related articles linked on that article.

I discuss language usage in the eastern domains in Hebrew Usage in the First Century

Question:
I have heard that the NIV Bible has attempted to "change" the word "Hebrew" in Acts 26 to the word "Aramaic."

Answer:
I am familiar with the situation you refer to and reference that in one of my articles.  The assumptions underlying the statement are highly misleading in saying that the NIV (or insert favorite translation that does not match your view) has "changed" a word.

This is a hackneyed red herring that various critics have speciously used for many versions, involving a long list of many various or phrases in the particular version.  This passage is very well known and discussed at extensive length by hundreds of scholars of various levels of sophistication.  It is not a matter of changing a word; it is a matter of interpreting the word/phrase in the Greek.

Two basic factors lead to this error.  First is a simplistic and erroneous concept of language.  This leads to imposing modern ideas upon the 1st century Greek language usages.  This leads to the second error.  These simplistic ideologues assume their conclusion then use that as an argument for its truth.  This is an invalid logical argument called begging the question.

In the 1st error, they assume this term/name means the same thing it would mean if we today refer to the "Hebrew" language as known in classical western academics.  Our modern use of the term "Hebrew" to mean the language now known as the classical biblical language is read back into the Koine Greek usage.

Violating Scriptural Integrity
The word in question here is not automatically referring to the "Hebrew" language as we use the term in our current setting for a specific dialect of Canaanite/Phoenician Semitic speech in which much of the Old Testament (Tanakh) was written down.  Writers of the first and second-century do no use any terms or names like that consistently.

Additionally the Greek term translated "tongue" or "language" in Acts 26:16 is dialektos (dialect or speech).  This is the word used in Acts 2:16, where on the Day of Pentecost, Jews from all over the world declare that they can hear the words of the Galilean Christians in their own dialektos.

We an easily read back into that era our highly detailed categorizing approach to information, which did not exist in earlier cultures.  This violates the integrity of the worldview of those people and their texts, such as the Bible.

Greek Usage
The second factor leading to the error is a logical fallacy that assumes an answer and uses that in the argument.  The whole question here is what the Greek phrase means.  The Greek phrase in question here is te Hebraide dialekto, which means "the Hebraistic speech."  The term Hebraistic was somewhat interchangeable with the term "Jew" as an ethnic term, and this phrase is equivalent to "Jewish speech," as my Yiddish taxi driver said about his language in New York.

The Greek usage does not reflect that this phrase is considered a technical name for any standardized form of speech.  Thus in this passage the NIV and most translations reference the overwhelming body of knowledge from various disciplines that tell us the common language of the Hebrew/Jewish people was a form of Aramaic, the descendant of which is still spoken in the area.

The facts of the matter prevent us from making a simplistic word-to-word association simply from the phonetic association of the name "Hebrew." The actual social, cultural and linguistic situation of the era provides the essential context for interpreting the meaning of that lone phrase.

An assumption of what the word referred to is not an argument for what it meant.  The question is still beneath each claim, and one did not "change" one word into another, but used one body of knowledge to interpret the Greek term into English.

Cultural Situation
Of course this leads to a different conclusion than Rood would prefer, and he claims a different assumption about the word and the cultural situation it refers to.  This does not address the cultural situation underlying the claim.  This is where I have been looking.  If we had lots of independent indication from unrelated sources that the biblical language or it near descendant was in fact still spoken, this would be a strong support for a claim of what "the speech of the Hebrews" might have meant.

So, you see, the word itself does not tell us anything, without the broader cultural context.  Words always have meaning only as they are used in a particular historical, cultural and worldview context.  That is just the way language works.

It is that context that we are probing to clarify the likely meanings.  We find many indications that the speech of (Palestinian) Hebrews/Jews and Galileans or Samaritans was Aramaic.  But no indication so far that it was Hebrew.  And lots of indications that Jews living outside Palestine used Greek as a mother tongue or primary language.

Greek Target Audience
One major problem is the contexts in the letters of the New Testament.  The places they are written and the kinds of questions they deal with could hardly be conceived to involve Hebrew speaking people.  No Hebrew documents from the era have been found.  Besides the total cultural milieu is Greek, whether Jewish or pagan.

So far I have not found any evidence that Hebrew was used or that any document of the New Testament was ever written in Hebrew.  I have seen many claims on Rood's site but no evidence.

Many authorities discussing these questions are online and in print.  I link to many of them in my various articles and my reading lists.
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*You will note the reference here to the temple this colony built.  This indicates they had no qualms about building a temple for their use, and did not continue focusing on the temple in Jerusalem.  This seems to indicate that the uniqueness and exclusivity of the Jerusalem temple had not yet been established.  This is consistent with other indications in the biblical texts that temple-centered worship had not, in fact, been universally implemented until after the Babylonian Exile.  Scholars comment that other older aspects of Hebrew worship also persist in Elephantine in contrast to the "intertestamental" Judaism that developed before the First Century.

OBJ

Also related:
Greek and Aramaic Among 1st Century Jews
Hebrew — The Original Language? (Of Course Not!)
Hebrew Usage in the First Century
Jesus' Knowledge of Greek: The Role of Language and Motif in the Fourth Gospel Narratives
The Language Jesus Used
Peoples and Languages
Textual Themes and Language Variations in the late Prophets
That Abominable Greek?
Thoughts on Aramaic Primacy:  Was the New Testament first Written in Aramaic?
What Was Koine Greek?

Related on the Internet:
The Greek History of the Middle East from 330 BCE.  Brief Historical Background To The New Testament
Exile — Jewish Virtual Library
The Greek History of the Middle East from 330 BCE.  Brief Historical Background To The New Testament
Jewish Funerary Inscriptions in Greek
John D Harvey, Listening to the Text: Oral Patterning in Paul's Letters
The Plot to Replace the Greek New Testament (Exposé of the "Hebrew Roots" Movement)
Problems with the Hebrew New Testament Theory
A Rood Awakening — Michael Rood
Shaye J D Cohen, From the Maccabees to the Mishnah (Philadelphia:  Westminster Press, 1987)

OBJ