It's probably not the sprinkler head, but a valve that's not shutting off.
A double check valve is a water backflow prevention device.
Water will flow in one direction through the valve but not backflow.
At the point where the sprinkler system's main pipe is connected to the potable water supply.
There may be a leak in the pipe or valve.
Either the water meter main is turned off or the master valve is not working.
Yes, valves can be located with a valve locator.
Depending on the size of the sprinkler system, normally just a few days.
Rotor heads will cover a larger area than the spray head.
When 1/4" rain occurs or temperatures reach 37 degrees, the timer will shut off.
Normally just a couple of hours.
It depends on the size of the yard to be covered and the meter size.
Depending on the size of your lawn, the time will be determined after the sprinkler system design.
Absolutely, a sprinkler system properly designed can save up to 50% of water usage.