I think I understand what you're asking but if I'm mistaken hopefully you will correct me.
- Yes, it is entirely possible for two opponents to sit down across from one another playing the same faction--both players could be playing Stark. This has no impact on the game, they just play their decks as they normally would.
- Yes, it is also entirely possible for one opponent to be playing Tyrell, the other playing Lannister, and both of them running the agenda "Banner of the Wolf" and running Stark cards. Just as before, there is no effect.
- Your Unique cards don't impact my Unique cards in any way. We could both play our copies of Ned Stark and use them normally. If my copy of Ned got killed and was in my Dead Pile, it wouldn't affect your ability to play your copy of Ned.