Did Moses have a second wife?
No, Moses did not have a second wife. There is no mention of Moses being married a second time or any mention of Zipporah's death in the scriptures. Zipporah was not a descentant of Cush, the son of Ham,Cush was the forefather of the Ethiopians. In Exodus 18:1:4 we read that Moses father in law Jethro, was a Midian and so was his daughter Zipporah.
Jethro, Moses’ Father-in-law
1 "Now Jethro, the priest of Midian, Moses’ father-in-law, heard of
all that God had done for Moses and for Israel His people, how the
Lord had brought Israel out of Egypt. 2 Jethro, Moses’ father-in-law,
took Moses’ wife Zipporah, after he had sent her away."
3 "And her two sons, of whom [a]one was named Gershom, for Moses
said, “I have been a [b]sojourner in a foreign land.” 4 [c]The other
was named [d]Eliezer, for he said, “The God of my father was my help,
and delivered me from the sword of Pharaoh.”
Paralleling - Cushan and Midia
In Habakkuk 3:7 we read : "I saw the tents of Cushan under distress,The tent curtains of the land of Midian." The paralleling of Cushan with the land of Midian indicates that Midian was possibly also known as Cushan, hence it is most likely that it is in that sense that Zipporah is referred to as a "Cushite".