First the Faucet that controls a tub shower wouldn't turn on. After some struggle I was able to free it, but then I couldn't shut it off. So I shut off the shut off valves behind the wall. Then when I removed the faucet guts, the water started runnig again leaving me to conclude that the hot water shut off valve would not shut off though the cold water does. So is it possible to disassemble the shut off valve and replace a part inside, like a washer, or will the entire shut off valve have to be replaced?
If it's the hot water valve and your cold water supply to your water heater has a shut-off valve, you can shut that valve off for the hot side only to repair the hot water shut-off valve at the tub. If that shut-off valve leaks, then you will have to shut off the main.
Depending upon the type of hot water shut-off valve you have at the tub, you may be able to easily repair it with a new washer on the end of the stem, or you may need to replace it.