In another timeline or maybe 6 months ago, I'd have the patience to explain, but right here and now not really. Whedon tries to do what I would best describe as Grimdark-Lite. He eludes to nastiness, but never fully commits to it. I guess I'd liken it to doing Mad Max versus The Road.
Mad Max is a lot better than The Road, though YMMV is always true. So in my personal opinion, I'd rather have grimdark-lite, I guess.
Firefly had absolute shit for world building. Wasnt it sorta retconned that they were actually in a giant solar system around a single star or some nonsense? But how the hell do you "erase" an occupied planet from a solar system? Any telescope would see it and they would still have to account for its mass.
Or why everyone spoke pidgeon chinese but there were almost no asians?
I loved the show but almost nothing about it really holds up. Doesn't need to, the characters were great.
Your first point is fair, I think it was changed after the show was cancelled, for the wrap-up movie. Also, fitting everything within one system snaps any suspension of disbelief, as the planets and moons would be 90% + uninhabitable, terraforming or not, as there's only gonna be so much real estate within the goldilocks zone. So all of the planets/moons would have to be basically within the same orbits for it to work.
Your second point is pretty easy to wave off or explain, as the show didn't explore much of the setting. There could be all sorts of other worlds/regions other than what was shown. Also, the US/Chinese culture blend could have happened before leaving Earth for this new system.