As for the mushroom, Celica needs wings for this. The bartender gives advice on this topic.
About Domenea - this may be a bug in your version of the game, it should work fine in the next version (0.69).
Just in case, treat Celica to a couple of cakes from the store in the dwarven city. Perhaps Celica has traces of demonic magic on her that are interfering with some quests.
Regarding the question marks: perhaps you didn't pay enough attention to Nel and Glace. Only the lady with the crystal ball will help here.