I have a little experience with these. Yes, connect phone as you described. Programming is via doorking for codes and options. The manual is pretty detailed. As for integrating with C4, yep, you have to use a relay. There are a couple of places you can connect it. One of them allows latching. Hold relay closed and the gate stays open indefinitely or until someone closes it via the phone or 1812 keypad. Open relay and the gate closes after its normal programmed delay. Close the relay momentarily and the gate opens and then closes after normal delay.

I believe we used a pair on the same cat5 that was already run for phone. Has been working fine for almost a year.