I think Gumgum is his own dad, as in a wizard Hiding in a younger version of himself, but something went wrong and he forgot who he really is. Now he grew up with Bart (who may or may not be his guardian, who may or may not also be brainwashed).

Edit: or gumgum is diah. I was thinking about this. Dia does seem to be gone from this plane and gumgum seems not too smart anymore so maybe instead of he being his own dad he is actually the goddess diah unknowingly. I was mostly thinking this because they almost have all the diagems and was wondering how it could be like memory pieces for gumgums campaign... Then at the end he turns into this powerfull magical Goddess and that's why he thinks he's a wizard. Bit farfetched ,but you never know with Mika's brain