1. Listen (a lot) to speakers/recordings of whatever accent you like

2. Read (a lot) of anything you find interesting

3. English grammar = memorization. We inherit grammar points from Old German, Old French, and Latin. The result is that native speakers mix and match grammar rules and it sounds weird when using a certain rule in a place where it logically should be OK.

It sounds like most of these problems can be solved with bulk exposure to the language. I know, easier said than done.

Also for the grammar, it would be good to have structured learning rather than just listening/reading to random things. https://learnenglish.britishcouncil.org/en/english-grammar/v... seems to be a decent resource, and British grammar is 99.99% same as American.