As I understand, the Jews descended from the tribe of Judah, which was the primary tribe in the southern Kingdom of Israel (along with the small tribe of Benjamin). Unlike the northern tribe, which intermarried with other people, Judah remained pure. The people of Judah became the "Jews." They were later overtaken by Babylonia (present day Iraq).
Thus, Moses was a patriarch of the Jews, but was himself from the Levite tribe, which eventually settled in the north.
I believe the Levites were dispersed among all the tribes as teachers and priests. They were the 13th tribe, making 12 when they were assigned.
There's no evidence that the other 10 tribes intermarried after they were captured by the Assyrians. There is evidence from Assyrian tablets that they allied with other peoples, placed on Assyria's northern border to guard it, to overthrow the yoke of the Assyrians. I'd assume that the House of Israel tended to stay together, like Judah.
