1.) Can Marika steal from their room? What about mugging them?
Yes and yes! He can't really fight back, but he'd talk all the way through that mugging.
2.) If so, what can she steal? Would your character eventually want it back?
His wallet? He'd like that back. And piles and piles of werewolf lore. Which he also wants back.
3.) Is there anything I should leave alone and have her ignore?
No, there's not that much in his room.