The symptoms you describe are all suggestive of a charging system that is not oerpating properly. There are many electrically operated devices in your car, including the ignition system, fuel pump, fuel injectors, and engine control computer. If teh lights dim when the brakes are applied, this is indicative that the battery voltage may be low; when operating normally the charging system should be capable of supplying enough voltage to keep everything running properly. If teh charging system is not recharging the battery, then the lights will dim at low engine speeds or when additional electrical accessories (like brake lights) are turned on. Also, when battery voltage drops low enough the engine will begin to run poorly.
I would suggest that you may want to ahve the charging system checked to make sure it is operating properly. Any repair shop can do this for you quickly and easily. Also, some auto parts stores offer free charging system testing, but you should be aware that the guys at parts stores are often untrained and do not know how to test the vehicle's electrical systems correctly; as a result they often try to sell you unneeded parts.
Chances are you ahve a failing alternator, or some other charging system problem in your car.
I hope this is helpful!