Did the Hebrews come from African heritage?

Answer 1

No. Any such speculation is based upon wishful thinking or lack of research. It crops up from time to time but has been debunked by DNA testing.

The Israelites were not related to, nor did they "mix" (have sexual relations) with the Egyptians (Rashi commentary, Numbers ch.26).

Just as today, Israelites came in differing skin-tones, heights, and body-types. Our tradition is that the twelve sons of Jacob (the 12 Tribes) were not completely similar to each other in appearance, though none of them was really dark-skinned (Rashi commentary on Genesis 12:11).
Abraham and Sarah came from southern Iraq and their wider family from northern Iraq. Since DNA tests have shown that Jews intermarried infrequently throughout history, Abraham and his Israelite descendants, including Moses, probably looked like Jews today.
DNA testing of Jewish communities worldwide has shown that they are all interrelated and of Middle Eastern genetics, not African or Egyptian.
In 2000, the analysis of a report by Nicholas Wade "provided genetic witness that Jewish communities have, to a remarkable extent, retained their biological identity separate from their host populations, evidence of relatively little intermarriage or conversion into Judaism over the centuries. The results accord with Jewish history and tradition." (See: What race were the Israelites?)

The only exception to this is the Ethiopian Jews, who show only a trace of DNA connection to other Jewish communities. Western ethnologists today hold the view that the Jews of Gondar (Ethiopia) either emerged from a Judaizing strain among Ethiopian Christians, or were converted by Yemeni Jews who crossed the Red Sea. A study by Professors Lucotte and Smets has shown that the genetic father of Beta Israel (Ethiopian Jews) was close to the Ethiopian non-Jewish populations. This is consistent with the theory that Beta Israel are descendants of ancient inhabitants of Ethiopia, not the Middle East. Hammer et al. in 2000, and the team of Shen in 2004, arrive at similar conclusions, namely that the DNA of the Ethiopian Jews probably indicates a conversion of local populations.It has been estimated that this happened some 2,000 years ago.

See also:

Are the African-Americans from the lost Israelite tribes?

Answer 2

No. They came from Western Asia, from east of the Jordan River.

Answer 3

The father of Egypt, was a son of Noah.