Abraham was a Hebrew. He wasn't called an Israelite, because he was the grandfather of Israel (Jacob) and his children, the 12 tribes of Israel. He wasn't called a Jewish man in his time, but because he practiced Judaism, Jews refer to him as the first Jew.
He was definitely Semitic being a descendant of Shem (who was a child of Noah).
Abraham's genealogy goes like this ("^" represents "a male child of" for those underneath):
Noah
^
Shem
^
Arphaxad
^
Shelah
^
Eber
^
Peleg
^
Reu
^
Serug
^
Nachor
^
Terach
^
Abraham
Judaism's roots are in the Hebrew religion of Abraham; and in the Israelite religion of Moses. According to tradition, "Judaism" as such began with the covenant between Abraham and God.
Monotheism.See the Related Links.Link: Who founded Hebrew monotheism?Link: What do Jews believe about God?
But they are the same people.
Israelite or Hebrew.
Joseph was a Hebrew, an Israelite.
Abraham is called a patriarch because he was one of the three forefathers of the Israelite Nation.The definition of patriarch is: "One of the scriptural fathers of the human race or of the Hebrew people"
There's no such designation as "Black Hebrew Israelite"
Jew, Jewish, Israelite, Israeli...
Black Hebrew Israelite
That depends which migration. Abraham migrated with his Hebrew family from Ur to Harran and then to Canaan (see Genesis ch.11-12); Jacob led his Hebrew (Israelite) family, descendants of Abraham, to Egypt (Genesis ch.46); and Moses led the Israelites from Egypt towards Canaan.
they didn't "become" Hebrew. They started out as Hebrew, because Abraham was a Hebrew.
Pharaohs in the book of ExodusThe book of Exodus tells how the Israelite s are enslaved in Egypt and eventually escape under the leadership of Moses. At least two pharaohs are involved, the "pharaoh of the oppression" who enslaves the Israelite s, and the "pharaoh of the exodus", during whose rule the Israelite s escape. Abraham means "the father of a multitude" (Hebrew: ʼaḇ-hămôn goyim) pharaoh the king hears of the beauty of Abraham's wife Saharan and whose jalousie.