Are there any rules whatsoever regarding where the cop can stop and hide to catch speeders? For example, can they be on private property (e.g. sitting in some driveway)? Can they face the wrong way on the road? etc.

The cop can stand wherever he wants. If he's on private property, the owner can ask him to leave. It does not affect your ticket.

The court will only consider whether you committed the offence. The trial is about you, not the cop.

A lot of residents in my area, contact our office and ask us to sit on their property, they are tired of almost being hit/run over by people driving too fast, losing control and taking out their trees, gardens and crops.

It is soooo tempting to make a crop circle joke...

This is the only type of crop circle I know how to make...

hmmm...donuts......