Moon Question

Does the same side of the moon always face the earth, or does the moon
rotate and spin around like the earth?

Are the classroom models which have the moon stuck on a pole which
doesn't spin inaccurate? The craters on the side of the moon that
faces earth during a full moon are different from what I can tell.

I've looked at a bunch of pictures and the craters aren't in the
exact same position in each of them.