I have a two handle american standard shower faucet that is from the late 60's. I replaced the valve on the hot side, but still have a drip. Two weeks later the hot water stopped coming out. With the stem removed from the wall, I can see a part in the wall that moves like a bearing, is this the seat, and is it supposed to be separate form the valve? It seems that when I close the fauced, it bottoms out.
Should any parts move inside the wall move once the valve assembly is removed?

No, there should be no moving parts once the stem is removed. Sounds like you have either a loose seat, or a stripped seat. If stripped, just as well look at complete faucet replacement and be done with the headache.