1) There's no time limit listed for sustaining a spell, so you could cast one into an appropriate sustaining focus (each category of spell requires a different focus, and the force of the spell is capped by the force of the focus) and let it stay up forever. Until something else happens.
2) If you're sustaining a spell yourself, you suffer a -2 dice pool penalty to just about everything else. You can still do other stuff, but you lose 2 dice. But some things might break your concentration (SR4A, 184). If a sustaining focus is doing this for you, there's no penalty or distraction.
3) Yes. But I'm not sure what kind of action, if any, would be required to move the target (you, in this case). Maybe the sustaining requirement is enough of a penalty, or maybe some GMs will treat it like moving a spell effect as a Complex Action.
Incidentally, it is possible to use the Counterspelling skill actively to dispel a sustained spell (SR4A, 185, bottom right). That's a problem if you're levitated a few dozen meters in the air.