I wouldn't be surprised if this was right, but that's probably the point of creating a separate identity for the Jewish people; to reject what their captors and those around them had considered normal. To hold themselves to higher standards.
Don’t know about that. What happened to Sodom and Gomorrah seems like a very overt communication of a prohibition, imo.
As I understand it, the Canaanites, whose land the Israelites were destined to occupy, were into all sorts of degeneracy. Therefore, all these rules were handed down by God, through Moses, to make sure that the Israelites didn’t absorb bad habits from the people around them.