Remote Wireless Tripwire
This sounds very doable. The first point, tuning the distance threshold at startup, could be done with a bank of DIP switches or a potentiometer on an analog pin to set the value. You might include some startup code continuously pings the transducer and displays the result on an LED, until you press a button to tell it "use this".

The second, is a very typical communication technique - sending "hello" packets periodically to confirm that communication is up. In your case, the same packet could carry a hit/no-hit bit within it.