I believe strongly that distinctions between dialects are a good thing, so I do not think of either American English or British English as being "wrong," but rather different reflections of the English language.
But, I've noticed that some Brits assume that since English was born in England, their forms are the only correct ones. American English has actually in many ways been more conservative in its grammar and lexicon, maintaining many original constructions that were lost in British English. This happens often when dialects arise following the spread of a language...I am told Quebec French is the same way as compared to the French of Europe.
So, I wanted to just point out a few things, because I am pretentious jerk who loves language and loves to point out linguistic misconceptions.
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3: Two-time and three-time make more grammatical sense, as using words like "double" and "triple" is inconsistent, because the construction fizzles out as you go on, most people stopping at "quadruple" or "quintuple" (ew). German, at least, maintains consistency in this regard.
Though I honestly prefer the sound of "single," "double," "triple," etc.
11. "Transportation" is good, because it creates a visible distinction between a noun and a verbal form, a distinction that often does not exist in English. I prefer the distinction between "transportation," which is unambiguously a noun and "transport," which then could be used solely as a verb (though it isn't, even by Americans).
15. The case of "Gotten" is similar. Think of these forms: I go, I went, I have gone. I write, I wrote, I have written. The -en suffix indicates a specific combination of tense and aspect. Unfortunately, it is often lost (I say, I said, I have said). "Gotten" retains a distinction in form that American English has preserved.
"I've got" in American English usually (though I am only speaking from my experience) means "I have."
16. "I'm good" is grammatically correct. You do not usually use adverbial forms after forms of "to be." Would you ever say "I am happily" or "I am sadly"?
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As for the rest, lexical differences between dialects are to be expected and are completely fine. I would never say "shopping trolley." To me that sounds so...awful.