Just to this specific point:

I'm curious if the use of the word shaitan in Judaism/Christianity/Islam is in any way a response to the name being the chief angel of a rival belief system

Within the Hebrew Bible, Satan isn't really a villain in the "Lord of all Evil, mu-ha-ha-ha!" sense, but functions more like Yahweh's own prosecuting attorney. The word "satan" actually just means "opposer" or "accuser."

In the story of Balaam and the Angel, that angel describes himself as... well, either Satan or a satan (small-s): lesatan, לְשָׂטָ֔ן.

False gods of the sort you're describing from around this time would be Baal (which means "lord" - there were several baals of neighboring cultures) or Moloch (which may be from the word for "king").

Islam (IIRC) views man as being made of clay (Adam has linguistic links to various semetic words for clay) while the Jinn are made of fire. Both humans and Jinn are endowed with free will. Jinn can be of any religion and are not always either evil or good. The Peacock Angel has a lot in common with some Gnostic ideas where the God encompasses both a dark and light side.

I don't know anything about the yazidi religon but the only relevant think i know in regards to the peacocksin Islam is The iblees is the leader of the shaytaan, the bad demons. When iblees was banished from heaven he took t and talked a peacock which was in heaven to let him, the peacock agreed. And maybe because of this peacocks are considered not to enter heaven after this.