I believe that The Entrapping Pharisee is unique. Most cards with the title "The [Something]" are considered unique (like The Strong Angel), and usually if there is a question on the uniqueness/genericness of a card, it is on the identifier (it is not). So only One TEP is allowed in battle at a time.
1) The 1/3 Pharisees bring in all possible targets, or none. So once one TEP is brought in, the other is no longer a possible target, and thus only one enters battle.
2) Irrelevant.
3) They can't both be brought in, but if they could, then the first one would capture, and the opponent either allows it or discards to stop it. Then the second one captures, and the opponent either allows it or discards to stop it. The opponent would have to discard two cards to stop the abilities of two TEP's. The power of his ability is what likely made him a unique character, so as to avoid 5 of them joining a T2 battle.
4) True that.
I haven't played teams, but I'm guessing that occupied sites would be shared, since they are in the LoB, but unoccupied sites aren't shared, since those remain in territory.
