Bluetooth should not really be a problem in the aircraft and also works in the mobile phone's flight mode.

I think so, Bluetooth is normally allowed

In short: Yes, most of the time.

Long: Most on-board entertainment systems use a combination of a 3.5mm plug with stereo signal (insert adapter here) and a 2.5mm plug with voltage on it. With these systems, this can be plugged directly into the 3.5mm socket.
Bluetooth is currently permitted on most flights and is therefore not a problem.

Further input: the entertainment system can often be accessed via Wi-Fi and you can watch films from your own smartphone, tablet or laptop. Some travel companies only rely on this.

If in doubt, check the information page of the relevant airline.

I don't know that