Hebrew

Hebrew is the designation for things pertaining to Abraham and his descendants, including the ethnic classification and the language. Derived from the word "_ABaR," meaning "those from across the way", it would come to be used only of the people and language of Israel. However, it had been used to describe the early Patriarchs of Israel that founded the ethnicity.

All the Old Testament up to near the time of the exile was consistently in Hebrew. Portions of the later prophets were written in a dialect of Aramaean which had become the language of the Assyrian empire and adopted by the Babylonians.

Ethnicity
Moses first used the full term "Hebrew" when referring to Abraham when setting him apart from the inhabitants of Canaan. This demonstrated a use of the term as a separate ethnicity. On the other hand, Potiphar's wife, an Egyptian, called Joseph a "Hebrew," which means "across the way," knowing that the slave had originated from Canaan which was across the Sinai desert from the fertile Nile valley. Joseph himself even referred to his homeland as "Hebrew", and the servants of the Pharaoh of Joseph's time called Joseph a Hebrew for the same reason.

At the beginning of the Book of Exodus, 80 years before the Exodus occurred, the Egyptian government classified people being descendants of Jacob as Hebrews. Eventually the Pharaoh at the time became fearful that the Hebrew people would multiply and join their enemies in case of war.

As the Pharaoh became fearful of the potential threat the Hebrews presented, he began increasing their workload. When that backfired by causing a baby boom,  attempted a program of genocide by killing all of the Hebrew baby boys.

So all Hebrews prior to Jacob were not considered Israelites, but all Hebrews afterwards were Israelites and no non-Israelites were ever called Hebrew. Only those who were Israelite would be Hebrew, even if an ethnicity was also from Canaan, as the Israelite population was the only major ethnic group in Egypt that originated in Canaan across the way.

Language
Like all languages after the dispersion from Babel, the Hebrew language seem to have developed over time. However, since the term "sons of Heber" is used of descendants from Shem, it is reasonable to assume that God's favored line held the kernel of what would become "Hebrew."

Much is made of what God called things during the creation week, as told to, and then by, Moses. From this one might gather that the language predated the designation "Hebrew" by thousands of years.

The Sons of Eber
The original language of this apparently unbroken family might indicate that nothing changed in the line of Shem that goes through to Abraham. When Abraham encountered Melchizedek, priest of the Most High God, there does not seem to have been a communication problem. If this priest-king was indeed Shem, then "Hebrew" would be the language of "the sons of Eber" (also spelled Heber) of whom the patriarch was the progenitor. Whether Heber's nephews (sons of Joktan) spoke his language after Babel is unknown.

Designated a "Hebrew," Abraham spoke a distinct language among the Canaanites as he lived there. This language would be shared during his life to his eight sons and numerous grandsons. In the Messianic line, this would be Isaac and Jacob, leaving us with the "God of the fathers" speaking their language. Easy communication seems to have been common in Canaan, but down in Egypt, a bilingual Hebrew Joseph used an interpreter to speak to his brothers.

About 320 years later, Moses the "Egyptian" had learned the Hebrew language on his natural mother's lap. When he was over 80 he was writing down the text in the Torah in the "Hebrew" language with some Aramaean and Egyptian loanwords  thrown in. This is understandable since Abraham's in-laws in Haran were Aramaean. Some names in the lists in Genesis have "foreign derivation," indicating a faithful rendering of names taken from lists made available to Moses.

The Book of Job was written in Hebrew and the dialogue of Job, Eliphaz, Bildad, Zophar, Elihu is Hebrew. All of these people inhabited the Land of Uz and the book's events may have been concurrent to or shortly predated Abraham. Hebrew may have stemmed from Shem's ancestors and passed on to Aram and then Uz, with it also passing through Uz's nephew Eber. Sooner or later the Hebrew of Aram would have had to die as Aram's descendants lead to the language of Aramaic, not Hebrew.

Semitic Languages
The descendants of Shem ended up with similar languages. This is discernable in the use of Aramaic in the Old Testament. The Arameans, being descendants of Shem's son Aram (also spelled Ram). Abraham's kin were an Aramean (translated "Syrian"), though they were not technically descended from Aram (they were distant cousins, from Arphaxad).

When Moses gave instructions concerning offerings of thanksgiving upon entering the promised land, he tells the people to recall that Israel had gone down into Egypt as an Aramaean, thus equating "Hebrew" with the ancient land from which Abraham had come. The Aramaic language was closely related to that learned in Ur. Abram spoke a Semitic language that probably changed slightly in the four centuries before Moses was born. The "original" Abrahamic language had become the Hebrew of the Bible.

By the time of the Exile, over 800 years after Moses, the languages had changed so much that the people could not easily distinguish them. As time went on, Aramaic would replace Hebrew as the language of the Jewish people. The "Hebrew tongue" of the New Testament was a dialect of Aramaic with Biblical Hebrew being reserved for the Sanhedrin, Pharisees, Sadducees and the other Bible scholars of the day.