Battery warning light & your lights are dimming??? Sounds more like an alternator problem.

Put a voltmeter on the battery when the engine's running. Should be about 14.5v. If you turn on all your headlights & fans it should stay about the same. If not, it's your alternator.

Check battery voltage 5 or 10 minutes after you turn off the car. Should be about 12.5v. Then check it again after several hours, or overnight. It should still be 12v or so. If it drops too much your battery isn't good.

You might have both problems, but your descriptions sounds like the alternator...