I want to complete all the collections in my museum on my own. Can other players donate to my museum? Is there any way I can have the museum only accept my donations?
Players cannot donate to a museum that is not part of their own town. As such, the only way that someone else aside from your town mayor can donate to your museum is if you create another resident who lives in your town and donate that way.
No one can donate to your museum while they're visiting you because it's not their own town, so you don't have to worry about trying to "block" them from doing so.