got: yeah, the participle "gotten" is strictly USian. I'm not entirely sure what the differences are between got and lexical have otherwise.

Singular/plural: there is a rule for this! BrEnglish treats nouns referring to collectives (team, band, jury, Parliament) as grammatical plurals, while USEnglish treats them as grammatical singulars. This can be extended beyond words that have the collective semantics built into their meanings, so can say something like "England (=England's sportsball team) have lost again."

Things like "maths," though, that's just a case of the British term being morphologically plural where the US term is singular.