The above link will explain a lot of your problem.
The immobiliser is still active if you enter the vehicle with the key as apposed to the fob, it’s a security feature, it prevents someone just copying your key and driving off with your car. You need a diagnostic unit to change this, The settings can be changed to de-immobilise on the key. There are a couple of members near you that show as having diagnostics units that may be willing to do this for you for a small donation. Look at the map under the LandyZone International Rescue forum to find them.
As above, it sounds like you have a fault in/around the receiver module in the vehicle. If you don’t have a rear sunroof then it may well mean removing the full head-lining to access it in the first place.
Locking on the key means that only part of the security system is armed. Only locking on the fob activates the full security such as full dead-lock (you can’t smash a window then open a door) and I believe the ultrasonic alarm is not armed on the key either from memory. Useful if leaving a gig in the car as the alarm won’t go off but also the alarm won’t go off if someone reaches into the car/smashes a window either....