Can I change my keybind settings/controls mid-speedrun?

yes

You can, but it isn't recommended because some pauses are counted towards the time at the end. If you need to change something with your keybinds/controls, it is probably a better idea to do it beforehand.

Yes, but that'll cost you a few seconds even if you're good at that kind of thing.

Pauses only count against you if your run is supposed to be retimed because its a sub 13. otherwise it wont cost you any time