Ok, yes you can move that pulley by hand, but it should be a little hard to move; I would say, if its easy to move, its probably a bad tensioner
Start your engine with the A/C on; as the a/c compressor cycles on and off, watch for this to jump, a little jump is ok, a big jump with a constant flutter is bad.
If your squealing coincides with the a/c cycling, I would definitely say the tensioner is weak. (disclaimer) it can also be the ac comp. but with what you have said, I don't think so.
I would also take the belt off and spin the pulley with your finger, if it sounds like an old roller skate wheel; that is bad; should be smooth and relatively silent.
You can pick up a belt tensioner for relatively cheap. Not to hard to replace either