"R" lenses will mount on your F-1, but the aperture mechanism is different and won't couple to the camera. You'll have to use "stop down" metering if you use a "R" series lens on an F-1 (as you turn the secondary aperture ring on your "R" lens, match the needle with the index mark you see on the side of the viewfinder. Of course this assumes you're using the camera's meter).
The ping may be the lens stop-down mechanism. Try pressing in the stop-down lever and firing the shutter. If the ping goes away, or sounds different, that's the cause of the noise you hear. If you still hear the ping, one of your shutter brakes may be bad.
On the original F-1, the battery compartment is located on the bottom plate. Unscrew the slotted cover. On the F-1N, the battery compartment is located on the front of the camera.