Could we charge a superconductive magnet and use it as a source of energy?
Yes. The energy expended in producing the magnetic field can be recovered during the field's collapse, which occurs after the current producing the field is shut off.
For example, the amount of energy stored in the superconducting magnets that steer the particle beams in CERN's Large Hadron Collider is equal the the kinetic energy of a fully-loaded jumbo jet going 500 MPH. Shutting the magnets down requires dissipating all that energy, and if anything goes wrong during that process, parts of the collider will get blown to pieces in an instant.
Note that the energy stored in the magnetic field of a superconducting magnet did not get there for free. When running, those magnets and the machinery needed to support them consume as much electrical power as a small city, for which CERN pays the bill.
Yes, in the same sense that you can store energy in a battery and then use the battery as a source of energy. See for example this Wikipedia article.