Any chance the belt is not getting a good bite on the alternator pulley? You could try placing a boxed end wrench or socket on the alternator pulley and then try to turn it.
The pulley should not turn at all or it should be very difficult to turn.
The random dying at lights could be the system voltage dropping too low. In the old days one could drive a car across 2 states without lights on the battery alone and down to 5 or 6 volts.
Get them down to 10.5 or so anymore and they will quit.