Dolphin (sort of) emulates a Wii NAND's structure so the savegames are in the Wii directory. If you want to back it up, you can right click on the game (in the main window) then export the save game (so you can re-import it if something goes wrong).
I'm not sure what's wrong with your GC games though, so I'll leave that to someone else
I'm not sure what's wrong with your GC games though, so I'll leave that to someone else
