Should Washer Drum Spin Freely?

The spin basket on your washer should not turn freely. The basket has a brake to stop it when the washer turns off or the lid is opened. If the washer has an odor, you might want to check the drain hose.

Should washer agitator spins freely?

Yes, this is normal operation for the agitator to move freely in both directions after a cycle or just sitting there while not being used. From what your describing I recommend replacing the agitate dogs. These are small clutches that only allow the auger to rotate in one direction.

Should washing machine impeller spin freely?

It should move freely. However, some impellers may feel like there's a small resistance which when overcome allows the impeller to jump 180 degrees round. ... Without knowing how free an impeller should be it's hard to diagnose but if one is quite tight all the way round it is probably obstructed.