Plumbing – How to replace a non-removable hose connection vacuum breaker

Some may not even have it. You mention a well. If the well also provides your drinking water, then you should have a vacuum break. But if the well is only for irrigation then you will likely not have a vacuum break or back flow preventer.

Where is the pressure vacuum breaker (or other backflow device) typically installed in a lawn irrigation system?

Usually right after the main shut-off. So if you know where the shut-off is, the vacuum break should be right there.

Does it matter, as long as it is before the first sprinkler head? Or does it have to be before all the valves?

It is usually between the valves and the main shut-off.

Is it typically buried or is it usually above ground and elevated?

If it's a vacuum break (and it should be) then it needs to be above ground. If it's a back-flow preventer then it could be buried.

Would one ever be right at the jet pump on home well systems?

It's more likely co-located with the main shut-off than the pump.

Do they ever have pressure gauges attached to them?

Usually not.

you can take a pair of locking pliers (use good quality vise grips or something like that, and don't be tempted to use needle nose visegrips), the biggest pair you can get to fit, and insert the visegrips into the circular shroud. its called parrot beaking. the vise grips will stick straight out from the shroud (long axis of the pliers parallel to the axis of rotation of the valve. once you have a grip, and the size of the plier is important here - smaller pliers will fit further in, but larger ones tend to hold better for the next step. you have to find a compromise. once the pliers are in there and clamped hard, you place a screwdriver or drift punch through the pliers jaws (behind where its clamped to the valve) and apply torque. just go slow and watch for bending of the jaws away from each other. you dont want the punch to lever the jaws apart to the point they slip off the brass flats or worse, round them over. also be wary of rotation. some valve bodies have right hand threads, some left.