In regards to the brake lamp, if your parking brake is all the way in, perhaps you have a low Master Cylinder level. Simply check it out and refill as necessary. If not, perhaps a poor level sensor on the MC, or your parking brake switch is somehow messed up.

The battery, well don't know for sure, but perhaps your alternator is going out? or maybe your battery isn't charging anymore? Get them both check out for free at any local Checkers/Kragen's/Schucks or I think autozone will test for free too.