The hot water valve on my bathroom faucet makes a vibrating sound when I turn it on 1/3 open or 1/2 open. When I open the handle completely, the sound stops. I tried draining the water and forcing any air that could have been stuck in there, but the sound is still there.

Do this: Close all the way - then Open all the way - angle stops under the sink. If that doesn't help than you probable have loose, worn out, washer inside the hot water stem. You will have to remove the stem and replace the washer

Hope that helps

Milo