The 2-hole pickups are mounted exactly like the bridge with machine screws held with aircraft fasteners. These go into threaded metal inserts in the body of the guitar. As Mark said, turning clockwise will lower the pickups and the bridge.
If the pickup is stuck when you rotate clockwise, then it's reached the limit and you will need a shorter screw if you want the pickup to go lower yet.
With the string buzz, you should probably adjust the truss rod first, since the neck is the only thing that will move without you making a direct adjustment.