I own a 2000 VW Bug and I think my battery is low. Whenever I leave the radio on over night the car doesn't want to start in the morning, but if I turn the radio off the car will start just fine. Also when I unlock my car it automatically locks itself again with a min or two which used to be a lot longer and if I don't put the key in the ignition and turn it before it locks the alarm on the car goes off. Is this a battery issue or an electrical issue?

If the radio is left on it can drain the battery.not only that,on the second setting,it runs alot more than just the radio.the auto lock time can be adjusted with the obd system,and if the battery went dead,it probably went to the default time of 2 minutes.if it is the original battery and it is 9 years old,it could be weak.
have what is known as an AVR test done to see what shape the battery is in.

"Whenever I leave the radio on over night the car doesn't want to start in the morning, but if I turn the radio off the car will start just fine" Not to be rude but why are you even doing that??? Its not made for that at all unless u buy a really good yellowtop. The radio is draining the battery. Duh... its like leaving the dome light on overnight when u try to start it the battery is dead. And for the alarm sounds like u need a new alarm or it to be reprogramed

Both,the battery has been run down too many times and your radio have a heavy power draw,if you have an aftermarket alarm it may have something to do with the problem.