Can I reduce fire damage from spells, if I have fire resistance? Or does it only help with non-magic damage?
If the latter is right, what does the Elemental Adept feat mean "Spells you cast ignore resistance to damage", if damage from spells is already magical?
Fire resistance applies to any and all damage that’s called fire. This is described on page 197 of Player’s Handbook:
No ifs, ands, or buts here; damage of the indicated type is halved. So if your resistance says fire, and the spells says fire, the spell does half damage. Elemental Adept defeats that protection, however.
Later in that same section, Player’s Handbook even includes an example of fire resistance explicitly combined with nonmagical resistance:
This example would not make very much sense if fire resistance only worked for nonmagical fire, because then the fire resistance would be completely redundant.