Can the Collapsed Room land you in the Mystic Elevator?
From my copy of the rulebook:


  If an effect of another tile or card leads to the Mystic Elevator (such as the Collapsed Room or Secret Passage), the token placed by that effect stays on the Mystic Elevator tile even if it moves.


Emphasis mine.

It doesn't explicitly say that the token remains functional, but that clearly seems to be the intent.

I've also been able to find a reference to an FAQ clarification that says much the same thing, although I have been unable to find the FAQ itself.


  Mystic Elevator -- If the Collapsed Room, Secret Passage, Secret Stairs, or Revolving Wall lead to the Mystic Elevator, does the counter stay there even when the elevator moves?
  Yes. It's Mystic, after all.