I'm 24 and from Virginia, US.
1) I don't have any strong feelings about the British accents. Some of them are hard to understand, because I do not hear them often, but they aren't bad, just different.
2) British and American people are certainly different in some ways. We listen to different music, watch different TV shows, eat different foods, and so on. But we are also alike: We speak the same language, have similar political systems, and so on. I think the Americans and the British are more alike than, say, the Americans and the Chinese, but we are stilll different.
3) I think American English has an influence on British English, just as it has an influence on many languages. American English is a lingua franca, so it must surely have an influence on British English. But British English also influences American English. We get British TV shows, movies, and so on, and we Americans learn British English just as surely as the British learn our language.