I've visited somebody else's museum before, theirs wasn't complete. It didnt occur to me at the time, but if you can visit their museum, then shouldnt you be able to donate to their museum as well?
No, non mayor characters can donate only in the town they live in. Every character, mayor or non mayor can only donate in the same town it lives in. The only way to donate something would be to give the item to them, which will work with art, but I'm not sure if that would work with bugs or fishes.
You can only donate something to a museum if it's in the possession of a character living in that town. The only exception is art, since it can be dropped; bugs and fish can't be exchanged between players, so they can't.
Only if your character lives in the town that needs donations! If your character doesn't live in that town, then you can't donate, however, the mayor or any character in that town can donate, so just give one of the characters the item c: