Yes. They are a bigot
No. They're not a bigot
There has to be some bigotry involved if you're not letting them use your bathroom. Well, unless there's some unknown factor involved like them breaking into your house or your toilet not working. If that's the case, the question itself is bigoted
Nope. Just normal.
I wouldn't want a man in the restroom with me, especially if they look like a man.
Hell, I wouldn't want them in here either. Get their own bathroom if they aren't really either or.