about 300-400 years - languages are 'living' languages, they change over time; because of geographical separation and divergence of circumstance, events, history, two dialects progressively diverge. Effectively British/American 'languages' are just dialects

They are actually the same language - English - however there are just a few noticeable differences. This includes (a) pronunciation/accents (this is probably the easiest way to tell the difference if you can hear either of them speak), (b) spelling of some words and (c) perhaps the choice of words and phrases in daily conversation. There may be other differences but these are the only ones I can think of right now, sorry. Hope this helps you!