As the title says, is it possible to fully upgrade all the weapons, spells and perks?

In one run, no (don't know if you could by replaying stages, though). I didn't find all secrets, but you certainly won't get enough points to upgrade everything fully without cheats or exploiting. I do think you get enough upgrade points to get most of one side (magic or guns) though, and you can probably expect to have 4-5 perks by the end. Bro-tip: Get Student as early as possible. :v