Plumbing – Removing stuck kitchen faucet

From the way you describe it, it sounds like it's a regular gate valve. You might be able to repair it as you describe by removing the packing nut and replacing whatever is broken or stripped out inside.

The only exception to that would be a ball type valve, but those will just have a handle that makes only a 1/4 turn. Those generally aren't repairable, but then again they almost never fail either.

Personally, I would just remove and replace the gate valve with a good ball valve. Gate valves have a tendency to rot out or seize up from lack of use. I actually had one once that disintegrated in my hand when I tried to turn it off (spraying water everywhere and making a nice mess). Ball valves are just much more reliable.

Minerals in your plumbing system begin to build up on the pipes and faucets over time. Eventually, if not removed, the minerals can restrict water flow to a trickle. This may explain the decrease in water pressure from the kitchen faucet. To repair the hose sprayer: unscrew the piece were the water is sprayed out. It should un-screw counter-clockwise. Hold it up to a light and look for any blockage. Soak in a bowl of white vinegar or CLR or Limeaway, etc. After some time soaking replace the spray piece. Also unscrew the faucet aerator and flush out any debris that may have collected in the screen. To disassemble the faucet but after the water valves have been shutoff, you will first need to remove the handle. Look for a set screw on its back. Once removed unscrew the top cap. You should now be able to pull the faucet cartridge out of the faucet body (probably with some effort). Look into the faucet body for any foreign matter that may have lodged in the faucet ports. Similarly examine the cartridge. If possible have an assistant slowly open the supply valves one at a time while you hold a cup over the faucet. You just want to allow a moderate amount of water to flow from the faucet to flush out any blockage. When re-assembled confirm that each valve is fully opened.