Thanks for your questions!
In the rules, it says that you can't have a duplicate of the same card in your domain.
What happens if you use a card like divine law which draws the top card of the deck and puts it into your domain and this causes you to have a duplicate?
If this happens, you discard the card you just drew, and draw another one into your domain - check out the 'Divine Favour' section of the Card Guide (where this situation is covered).
Can you discard a citizen for cards that have a "discard a card from your domain" as a cost?
Yes, you can discard any card in your domain for these abilities - including Citizens.
When you trigger a card that has "other players get XYZ action", the rule says that other players get the action in turn order. If you are player #2, does that mean it goes 3,4,1? or does it start at the beginning and go 1,3,4?
When other players need to take actions on your turn, it always goes in turn order, starting with the player who has the #1 disc. So in your example, the active player (with disc #2) would take the action, then the player with disc #1, then #3 and finally #4.
Thanks for playing!