Base/supporters are synonymous, to be fair. Not sure what your point is.
Yes, for the most part, but I think there is a distinction.
Supporters might come and go based on multiple different criteria, your base is the core of your support, those whose interests and/or ideologies match closely enough with your own that you can rely on their support without hesitation.
I've said it before, you don't have to be a racist to support Donald Trump. Many who support him are NOT racists. But if you are a racist then Trump is your guy. Racists haven't had a stronger ally in high office at any point in my lifetime.