The fuel pumps can usually be heard buzzing at idle, if its only doing it sometimes you will probably find it stops when you start turning lights and blowers etc on, i wouldn't worry about it, just loading up the alternator, like when you turn the blowers or heated rear window on its common for the lights to dim slightly.

As for your ABS ive never had a car with it on and in the event i did it would be the first thing to come off. The buzzing will be the relay controlling the bulb IIRC, check the belt break switches are secure on the modulators.