I want a faucet that shuts itself off (saves h2o).

Assuming water is cut on at faucet, be sure hot and cold lines aren’t reversed. Also check screens in hoses and valve for debris.

Look for the obvious-take off the screen. Then you may have to venture into the faucet itself. If you have galvanized pluming, every time you shut the water off, scale will fall int the center of the piping without pressure and then when you open the faucet it tries to flow through small orifices.

Does same thing happen at all faucets?
Are you getting error code?
You might have crossover problem with defective faucet cartridge.
Copy following links for troubleshoot resources:
http://waterheatertimer.org/pdf/No-Error-Code.pdf
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Check the hot water shut off valve, when the washer fails sometimes the valve itself sticks closed, and sometimes the washer breaks up and clogs water passageways down stream...
To test, pull the hose off of the hot water shut off valve, open the valve and see if you have water flow. (route hose into a bucket, you need more that a small amount of water.....
If you have good water flow from the shut off valve, then you likely have a particle that has lodged in the passageways of the faucet. Reverse flow with air pressure and see what you get out....

In order to repair this faucet you will have to shut off water before it gets to the faucet. Probably whole house. Thank you

If you have pressure to the shut off valves then most likely your shut off valves are not fully opening, I would recommend you replace both valves, they build up water deposits in them a lot of the times. The other possibility is the faucet itself has a water saver filter built into it. A lot of the new faucets have water savers built into them now.

Yes, debris from water heater replacements often breaks lose and gets stuck. The problem could potentially be anywhere between water heater and the faucet. The faucets shut off valves or the Delta faucet cartridge itself. Turn the hot and cold water valves off under the sink and disconnect the water supply lines from the faucet. aim the water supply lines into a bucket and turn the valves on one at a time. If there is a significant reduction in the water pressure and volume on the hot water side, you need to replace the shut off valve. If there is no reduction in water pressure, you need to clean and/or replace the Delta faucet cartridge. Contact Delta to receive free replacement parts.

Clogged galvanized pipes. Replace with Pex or Copper lines. Or bad Moen cartridge- see department store for replacement or call Moen direct. You can get the # from gethuman.com

balancing spool on the faucet ?

if this is the faucet in picture, turn off water, pull out cartridge and inspect for any debris in cartridge or valve body, if not, turn on hot water to see if water is getting through valve body. May have kinked line or debris from or in angle stop line.