As it turns out though, Americans these days speak with an accent closer to the British of that time than modern English people do. While dialects vary throughout both countries, the accents in England have changed a lot more than they have in America. Read more about it at the link.
1. An accent only happens when someone is speaking a foreign language. A native English speaker talking in French has an accent. Dialects are variants of the speaker's native language. Southern American, Cockney, New York, RP, etc, are all dialects.
2. There's no such thing as a "British" dialect. What people mean when they say "British accent" is one of several regional dialects found in England. Within Britain there are Irish, Welsh, Scottish and English dialects.
Something to do with a German king who couldn't speak English the same as others, and like the Castilian accent, they all started reproducing that king's "errors".
I think the king was a George.