your chirping is the belt or a pulley is bad. take the belt off spin the pulleys by hand, the one thats not smooth feeling is the problem. idler, or tentioner). or the belt is shot, flip it over your finger and look for cracks in the belt.
the lights dimming is a bit normal as the rps drop at a idle the alternator cant keep up with the demand of power and then slows down a bit power wise.
you can get it tested for free at most parts stores, the battery and alt that is. you want to see 12 volts @ the battery when the car is off. it should read over 12 but not much more then 14.3 at idle running.
