The pump is supposed to run continuously during spin mode to pump out the water being spun out of the clothes.
Turning the pulley clockwise (viewed from bottom of pulley) simulates operation during spin mode. The entire transmission housing should rotate during spin mode. The basket is locked to the transmission so that it turns when the transmission does.
What is the transmission doing during normal spin mode?
There are several things that could cause your problem (bad motor, loose belt, broken LGS spring on transmission, bad cam mechanism on transmission, frozen lower bearing on transmission, clothes stuck between basket and tub, worn out basket hub, problem in control panel...). We need to narrow the problem down. I need detailed positive feedback from you.