Cd player comes on by itself in my Astra 2004 SRi?

Hi, I've had my Astra since new (late 2004) and a few months ago my cd player came on by itself. These past few weeks its been doing it a lot (and blearing out!) and my battery is constantly flat. I store my car in a rented garage so I don't know what's it's doing when I'm not there! It seems to come on when I either lock/unlock my car via the remote. Another fault is that last month i hitched my caravan on and the indicators on the van stayed on, naturally thinking the problem was with my van but it wasnt. I Plugged my caravan electrics into another car and all was fine. My bother-in-law put a meter to the black plug on my towbar and found that my car was putting out 12volts even though my car wasnt connected to anything!!!I called out Green Flag and he re-set the relay to my towbar electrics, metered it again and seemed ok on that occasion!. My car is going flat after one day after a good run around!!. I've got my car booked into Vauxhall and they have told me they want £82 just to look at it!! Hope you can advise please?