Do the sages teach that Cain came from the union from Eve and The Satan?
Yes, however, check out the Guide for the Perplexed, which explains the whole "lilith" thing and "snake poison" thing to be a metaphor for ignorance. Search sefaria for "cain" in the guide for the perplexed to find it.
The Zohar explains that there was a general improvement until the revelation at Sinai. Search the zohar for "seth" or "Shet" to find it, should be in parshat bereshit.