I just want to clarify, I remember hearing something that said that you don't necessarily have to capture every capital for domination victory if the capitals you haven't captured have been captured by someone else. In my current game, a CS has captured a capital. So I could still win domination victory without taking that city? Or does it work differently?
Also, when looking on the victory conditions screen if a capital has been captured by a CS it will say "this player has not settled their capital yet". Not even sure if that can be fixed however.
If there's another warmonger who has capture another capital, you just need to take the warmonger capital.
I believe yes.
The rule is that you must be the only person with your original capital.
Sadly this is not true anymore, with BNW the condition has been changed to "One player must control all original capital".
Puppets are fine but capitals controlled by allied CS or Vassals prevent the validation. I tested this back in february, don't know how it work with multiple players in one team though.