I am the other side of the UK and so do not know your area.
You mention "Alarm went off first night at 4am so we leave unlocked at present" and "screen which has just started to show doors open when they're not". This year I bought a CDTi Saloon Connoisseur SE with 86,000 miles and had those issues (and more) from serious rain water ingress. I had severe water ingress at two locations.
Firstly, under the saloon boot carpet and all around the boot. The wooden floor support showed a long term problem. I sealed the tail lights and boot side air vents, (and more), cleaned up the boot and have have dusters and towels over the parking module inside the drivers side rear wing. That stops the parking module getting wet.
Secondly, the more severe problem was the sunroof drain pipe end had shrunk and was not letting rain water reach the drivers side front wheel arch, but directing the rain water down near behind the bonnet pull to open lever. which means flooding the immobiliser unit so that the contacts become corroded and that causes car's dash display to do strange things even when the car is parked and locked. The alarm goes off and sometimes wipers start when the car is parked.
The fix is stop the rain water leak, dry the car and carpet, clean the electrical contacts of the immobiliser and reposition it to avoid risk of rain water ingress
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