Yes.
No. You cannot do anything when you rest except pick up the loot. It sounds like you're asking if you can pick up a loot, move to another room, then pick up 2 more loot and rest. If you rest in a room, you pick up (up to) 2 loot.
No, you can move through rooms with monsters as well as through rooms without monsters. Only when you stop in a room do monsters populate.
I don't think it's lame. I love being able to replenish my hand periodically to get new Screw This! cards and monsters - especially since Durkon rests periodically for his other shticks.
I'm not sure I understand the question. Players give Durkon loot and he flips his Cure Assorted Wounds shtick to heal them. It's voluntary for players to give the loot to Durkon for the heal. He can't force them to heal.