The monsters can be distributed into various rooms, and can be placed into those rooms in any order. They should be placed on top of any stack of creatures already in the room, though. Well, unless the monsters you're moving are pesky Demon Roaches, which skitter to the bottom.
It needn't be equipped - just show the other players that you're trading in the right cards.
The text on page 18 assumes you're attacking with the area effect shtick, but you attack and defend as normal when using area effect shticks. So if you move into a room, then you're defending (and cannot use Fireball, for instance.)
It boosts Hide.
The monsters stay there and fight. Similarly, if you move a monster into any room with Battle Size 0, it would remain there. The Battle Size pertains only to populating the room.
When they're gone, they're gone. That's motivation to finish up the game before the deck runs out.
You can still acquire shticks while the dungeon is collapsing (though it really only makes sense to trade in monsters, not loot, since loot is worth more victory points at the end of the game.) Xykon is worth 2 times the level bragging points (as mentioned in the FAQ.) You can trade him in for a shtick (along with another XP) but keep track that you killed him, so that you get the points at the end.
Every room in the dungeon is cleared of monsters.
Start at the bottom (Xykon's Lair) and work your way up. If you run out, do not use cards from the discard pile - the rest of the monsters just don't drop loot.
Screw This! cards are resolved in LIFO order. In other words, you can play a Screw This! card that negates, changes or amplifies previously-played Screw This! cards.
Demon Roaches go to the bottom of the stack as they're played.
I updated the FAQ a couple days ago to resolve the inconsistency, but didn't announce the change because we're still playtesting at least one other change that may go into the FAQ.
Cards are not removed from the battle, but the battle stops where it is, as IFTCDT is played, as you indicate.
They're one-shot only cards, so no.
No, you can offer as many loot as you want to players for assistance, regardless whether it's PvP or PvM.
Well I think people understand the spirit of the rule, but it might not hurt to put it in the FAQ so that the Rules Gestapo don't kick our door in.
As usual, Craig or Rich may have additional comments on this. Nothing's really officially official until it goes in the FAQ.