[Qsilver7]

The driver’s door should not be lockable when it is open (its a BMW anti-lockout feature that goes back decades). So any attempt to push the door lock pin down when the driver’s door is open…is NOT a sign that something is wrong with the doors. It always needs to be closed before you can manually lock it or lock it using the remote fob.

The other passenger doors can be manually locked (door pin pressed down) when they are open.

And yes, the fuel filler flap/gas door is part of the central locking system…and if it is not working properly, it can affect the central locking system.

Back a few decades…if the fuse for the fuel filler flap blew…it would cause central locking not to operate correctly…so check that fuse (probably is in the rear fuse box). Perhaps that fuse or one of the other fuses for central locking is blown.