Note that "make choices" is a little broader than "choose targets."
The correct answer should be #2. The first player indicates his intention to put a character into play (by either revealing the character or declaring his intention to not put a character into play), followed by the other players indicating their respective intentions in player order, then the indicated characters enter play simultaneously.
It's like Arianne. You indicate your intention by revealing the character you intend to put into play, even though that character doesn't leave your hand for another 4-5 steps. You reveal the card in order for all players to ensure that all of Arianne's play restrictions are being met. The fact that Bitterbridge Encampment doesn't have any play restrictions on the character doesn't change the process -- after all, there could be an external effect imposing restrictions on the character entering play.
I don't understand. There is literally nothing in the RRG that in any form would say that "when an effect instructs you to put a card into play, you need to reveal it first". For Arianne and the like, the rules were interpreted as requiring to reveal a card to prove that you can actually resolve a triggered ability and change the game state, before your opponent gets to decide whether to cancel it. This makes sense. But this is not the case here. Why then is it "like Arianne"? What part of the rules would suggest, directly or indirectly, that I need to reveal the card before putting it into play, specifically as part of resolving the post-then effect?
I can see how "make choices" would be broader than "choose targets". Still, the quoted RRG entry only says that the first player needs to make choices, not that he needs to make [everything related to these choices] public knowlenge. Why can't the first player just announce that he intends to put a card into play, and set the chosen card aside, just like we do it with plots - why wouldn't this satisfy the rule from the quoted entry?
I guess the first player could put a dead character into play (another copy in the dead pile), see what his opponent did, announce his mistake, and try to put a different character into play. Revealing a character first would make sense then. But I really think this needs to be in the FAQ.
The process of "Initiating Abilities/Marshaling Cards" explained on page 10 of the RRG doesn't cover Resolving abilities (post-then effects and/or abilities initiated by your opponent), nor Ambushing.