[Disco 2 sticking central locking]

Door lock- sound like the solidoid is needing replacement or lubricatinf the push rod may help

Rear door handle= Worn return spring, replace the whole thing from ebay cheap fix...

[Discovery Alarm/ Central Locking]

This does sound like a problem with the imobiliser rather than the alarm. I would suggest that its checked out by a dealer because it could be the symptom of things to happen. Had same problem on a VW passat and the engine cut out on me, not scare mongering or anything but...

[Tail Light Inoperative 300TDI]

I have a Discovery 300 TDI 1998, where the rear off-side tail light (bumper) is not working. I found that the bulb had blown as well as the fuse and off-side front side light. Having replaced all bulbs and the fuse the rear tail light still does not work. Any ideas on this one?