I've started playing the new Tiny Death Star game lately and there are special characters that come every now and then (Princess Leia, Han Solo, Boba Fett, etc). Is it possible for them to move into a residential level? Whenever they're on the elevator, they have a '?' above their head. Sometimes, they chose to go to residential levels, but they're either full or not finished building. Is there any chance that one would move in or is it impossible?
It's impossible. They will never ask to go to a residential level with any spaces remaining, and the question mark behavior means you can't even be sneaky and evict someone after you see which floor they're going to.
Those characters are only there to patronize shops and unlock scenes, and it wouldn't make any sense to have a Boba Fett living in your tower and then have another one show up so you could unlock a scene with him.