You can flush the head by removing the nozzle and turning the zone on for a few seconds. If water comes shooting out, then the blockage is either gone or was never the problem. Also, check the filter under the nozzle for debris.

shut off the water and remove the valve bonnet and solenoid. make sure everything is clean (the small opening at the base of the solenoid has a sharp corner, clean with water and air but not tools). reassemble. If there is a leak in the zone, there will be a puddle. it's that the problem, dig in the area of the leak and repair.

The recirc pump shoudn't be an issue if it was properly plumbed. Do you have too many elbows in the run? How about tubing size. Typically the main feed will be a minimum of 3/4" to the bathroom then 1/2" branches off of that. Could be a clog in the head or restrictor, try taking the shower head off the arm and see if you get good volume out of the arm.

Most standard plumbing to the fixture is 1/2" pipe, so that should not be a problem for the handheld. I agree, its either debris in the screen (there is usually one in the fitting behind the head), a flow reducer build into the head (it may be removable) or when someone tightened the head or hose down to the fitting they managed to mangle the washer so that it deformed and obstructed the opening. All of these are simple, cheap fixes. Bruce