For your first question: any language that's still in use is always evolving. It's a natural consequence of the way people acquire language - people typically receive some formal education at school, but it's overhwelmingly a process of learning via exposure and imitation. In simple terms, if a new word/pronunciation/grammatical form develops, whether from a mishearing or misunderstanding (imitation is rarely perfect) or through deliberate innovation, it may remain confined to the person who first used it and then be forgotten, but it may also catch on and spread further through the same process of exposure and imitation that generally governs language acquisition. More often than not, the former, but the latter occurs often enough that if you take two (or more) populations speaking one variety of one language and have them separated for a significant length of time, their speech will diverge. In the case of the regions you're talking about, the separation of (for example) American and British English started literally centuries ago. Even in today's world with constant media sharing and internet connection, the British and American speech communities are primarily self-contained, and that was even more so the case for most of the time we're talking about. By this point, it would be absolutely astonishing if they hadn't diverged to some degree.

As for your second question: to be honest, I kinda disagree with the premise entirely. So I'd like to answer it with another question, that might hopefully clarify: What do you mean by 'dialect'? The definition of exactly what makes "a dialect" is a tricky one - there's no canonical linguistic definition, if you ask 10 linguists you'll probably get 11 different answers - but I can't imagine any definition by which the varieties you mentioned wouldn't be distinct dialects.