sounds like a problem with your alternator. Autozone and similar places will test it for free but you'll have to pull it off your engine yourself. I'd also have your battery tested for good measure too.

The reason I say this is because your electrical gremlins are spread throughout the car from the exterior lighting, to the interior lighting to the engine ignition, to the abs system... the only thing they have in common is their power source: the batter and alternator.