Magnets can be suspended over superconductors because of the [tex]\Large\text{M}\ddot{\text{o}}\text{ssbauer}}[/tex] effect, the observation that magnetic fields are excluded from superconductors. They are excluded because any magnetic field will set up a moving current in the superconductor of sufficient strength (assuming it is less than the critical current of the superconductor) to repel the magnet and its magnetic field. Naturally, a magnet suspended over a superconductor is stable, it doesn't spin. However, they can easily be caused to spin (by simply nudging them in the right direction) and will take awhile to slow down since there is very little friction (since they are suspended, I would think it is mostly from air resistance).
As for the top, I am unsure of the source of the effect. It could be due to having released it at an upward angle (giving it a little vertical velocity), or maybe an aerodynamic effect where the movement of the air due to the spinning top imparts a little upward velocity (I doubt such an effect would be large enough to notice even if it exists.).
So, no, the reasons are not related (unless the top is magnetic and is over a superconductor).