the battery light is a new one to me.
The studdering stops usually result from one of two things. warped rotor or abs malfuction. if i were you ide double check the rotors first then start trouble shooting the ABS such as the dealership or attain a reasonable speed on a slick surface such as dirt or wet parking lot and try to push the brake peddle through the floor with emphasis on trying to break the pedal.
. if you feel the pedal shaking your ABS is functional. If your wheels lock up and you go into a slide your ABS is not functioning. Also listen for the ABS pump buzz in (turn on).
I know in the M3s the ABS system is designed to disable if it detects a faults in the circuit. may be something as simple as a sensor. dealerships can read any error codes in the ABS circuit.
the last time my ABS went on the fritz i went and bought a used ABS pump to swap with my faulty one after using the testing procedure above and not hearing my ABS pump. i was very lucky since that was throwing a dart in complete darkness. havent had issues ever since.