It really depends on where you are, I think in Europe the English taught at school and considered the regular one is British English, but if you take movies/series/music, the broader one is US English.
I suppose this depends on your school/teacher. Our English teacher went out of her way to always teach proper (British) English and point out any differences with American English sometimes with an history lesson added.
Quite a few. Spelling and pronunciation are quite different, and also a bunch of words and idioms that don't match.
Not enough to prevent mutual understanding, but it can get close. As an American, if I haven't watched any British TV for a while and try, there's a good few minutes where I have to listen to most of it twice to be able to understand what was said.