Yes, it is safe.

Yes. The only think "unsafe" (more like unhealthy for the battery) is to heavy use the phone while charging due to generated heat. BT uses very little battery, so it's totally fine.

you will turn in to hulk while doing this!

The only unsafe thing would be how loud they're

It should be okay, IIRC sometimes there's extra buzzing(interference)/heat/etc. though.

For TWS earbuds and Bluetooth usage, see here for more info: https://www.reddit.com/r/headphones/comments/10kai7u/should_i_keep_ear_buds_out_of_the_case_after/j5so87z/

Here's what I do with my TWS earbuds and TWS adapters (like FiiO UTWS3/5) or really Bluetooth/wireless/rechargeable/etc. stuff in general: I try to only charge it when it has no battery or will have no battery soon. And then I don't touch it at all while its charging.

Info about UTWS3/5 battery life (5-7 hours) and also TWS earbuds volume variability: https://www.reddit.com/r/headphones/comments/10yr7js/finaly_good_audio_on_the_go_utws5_and_fh5s/j803bbw/

For Bluetooth ANC headphones, those can take a while and yes, just leave them be, use a wired IEM/headphone instead or your speakers.

What makes you think it's unsafe?