The phone must be connected with Bluetooth, but can run in aeroplane mode itself (without 4G or Wifi)

No, must always be connected to the mobile

No. It works via the mobile phone's GPS, i.e. the location signal is received by the mobile phone and then transmitted to the Beeline via Bluetooth. I think it works pretty well.

You can actually do this if the route is saved.

Yes, that works well.

I don't know, I've never tried it.