1) yes That is what it does best, flicking a relay on and off from the PC.
2) If it has a remote line so it only turns on when that line is live yes. If it auto turns on when power is applied, then yes.
3) well the beeps are too slow for a frequency to voltage converter, and may be too fast for the FB unless you have a beefier CPU. I wont say "yes" just in case, but maybe.
We do however offer an ultrasonic sensor, and you can solder your own transducer on it if you want. This will output a voltage that the FB can see perfectly.