Extremely powerful fields can levitate a frog - so yes.

https://news.harvard.edu/gazette/story/2024/04/how-did-you-g...

Probably not in a useful way; the induced currents would produce far too much heat.

If it's strong enough, probably. I mean, MRIs kind of work that way.

Yes the 45 Tesla magnet in Tallahassee can levitate small non ferrous things like a strawberry in a little tube and draws 56 megawatts about 7% of the cities power grid.