There's a "bug" with democracy, slaves, and I believe the industrious trait, where things don't quite round the way they intuitively should. I don't remember the exact details, but it is NOT your imagination. Once you get replaceable parts, this little quirky behavior disappears.
Oceanus:
A) Yes, it determines (partially) how aggressive they are, what they like to build, who they like to ally with, etc. Similar cultural civs are slightly friendlier to start with, ally slightly cheaper, etc. Cultural background is not a really noticeable game effect, IMO, but it does play a role.
B) Well, civs from your cultural background will treat you a little bit more congenially than those from a different background, but it's rarely significant, in my experience. But, no, you don't get any benefits from following the "natural" AI tendencies for a civ (beyond civ traits, which are, of course, different and GREATLY affect gameply).
C) They're listed in the editor. I don't know them off the top of my head.
Finally, an alternate reason for the AI troops suddenly dying is that they couldn't support the unit and it died that way. I believe those deaths get full animation and a war declaration can sometimes trigger an AI cash crisis.
Arathorn