Yes. It would hang there. That was one of the demonstrations of why superconductors are so cool back in the day. I remember seeing those nitrogen(I think) liquid cooled super conductors holding a magnet above them.
I don't think so. If I remember the explanation, superconductors "block" magnetism, rather like having another magnet with the same pole opposed. In that case, the magnet would probably just fall as though the tube was made of plastic or other non-conductor. (Just speculation, it has been several years since I read about superconductivity).
They are diamagnetic i believe (so is water' very weakly so. - google for levitating frogs for a laugh.)
Diamagnetic materials create an equal field to what they are exposed to... Causing repulsion. In the case of superconducting, the field generated is very strong and why we can levitate any old magnet over a superconductor.
Levitating a frog (mostly water right?) takes some incredibly strong fields..... Liquid cooled bitter magnets etc....
Side note - rare earth supermagets are toxic. When they shatter, you dont want to ingest any of the bits/dust
