Yes, that decision is made by the phone (or it user). On my phone, that's relatively cumbersome, so switching the BT unit on and off is much easier, should the need occur.
It' probably just a decision made by the firmware programmers. Other devices may be different.
If I power off the phone to change SIM and then power up again, the BT connection is not lost. Maybe it has to do with the length of time the connection was interrupted or something.
Yes, that's correct.