If this valve is 22 years old then it is probably the solenoid plunger that has rusted or something in the solenoid's connection to the valve. The solenoid is there but is not opening the valve properly. It's probably time to change out the whole valve. I would clean it out and if that doesn't work, have it changed out completely.

when you turn the water supply off is there any water discharge out of the anti-siphon. If there is the blockage is further down the distribution line, if not then the PR is clogged. To answer your question, water will only discharge thru the outlet when the inlet pressure is released.

Plumbers putty or Silicone is only used to seal the Tub Drain Basket to the tub. The threaded joints on your drain pipe are "slip joints". If you have a brass waste & overflow kit the slip joints have a neoprene washer under the nut. If it is a plastic Waste & overlfow kit there is a nylon ferrule under the nut that effects the seal. The nuts MUST BE put on dry, no plumbers putty, teflon or other material that might interfere with the nut surfacing against the ferrule. Take the nut off and clean all the plumbers putty off the threads, then double check to make sure the ferrule is installed correctly. The ferrule has a wedged shape cross section. make sure the pointed part of the wedge is pointed towards the joint with the nut tightening against the wide flat side of the ferrule. As the nut is tightened the ferrule is driven in between the two pipes to effect the seal.

I am not a plumber. I started trying to fix the faucet that spurts out water when it turns to the hot side. The water spurts from under the handle into and then out from under it. Last night the pipes started to leak. It looks like it leaks from 4 places. The hose that attaches to the hot water drips. Three of the connections. Im willing to try it myself before we bring in a plumber and take the risk. We could go without the sink till this virus blows over. Here are better pictures marking where it leaks. When I turn on the faucet, most of the water goes down the drain. Some of it leaks frm where the pipes connects under the sink, the two parts where the pipes connect, and the hose for the hot water. The hose for the hot water I'm not sure where the leaks starts for it. I just see water dripping down it and dripping down. You're saying I should just replace the whole handle instead of using the warranty. If I leave that for last, how do I first fix the pipes that are leaking? Is it an issue that everything where the water hoses connect look rusted? This would be my first time doing something like this and its a good time to force myself to get it done. I don't have a wrench that is wide enough to wrap around the screw to tighten it.