Okay - i am back home now. Again i am not technically minded with cars (or much for that matter!) but I will do my best.
Yes door locks work.
Car drives okay with the alarm going off.
Yes - i believe they are 2 separate faults as the problem with the bulbs blowing was happening for a while before the alarm problem.
Battery is a new one as it was originally thought i needed a new battery as the previous was the original.
So... I took it for a drive for about 15 mins (ah..... I love driving this car!!!)
The lights were all working to begin with.
I then washed it with a jet wash.
I got back home and bulbs have blown (i believe there should be rubber caps on the back of the headlights but mine doesn't have any).
I haven't done any suggestions on this thread yet but I have taken some photos.