Should the crankshaft pully rotate well the car is not started?

Not freely. What motor do you have. The two common setups are the pulley is bolted to the harmonic balancer or the belt grooves are cut into the balancer. The balancer is secured to the crankshaft with a tapered seat and bolt with a key way to prevent rotational sliping. You will need to see what is damaged.

V6 3.0

Under normal conditions you should be able to turn the crank with a wrench on the balancer bolt but not buy hand. You should feel the compression of each cylinder. If the crankshaft is moving freely you may have timing issues or a timing failure

3.0 Looks like the one piece. Remove the belt. Does it move by hand? I would check the key. Usually you need a special tool to pull the balancer/pulley but if it is already loose it may come off easy. Try not to damage the seal in the timing cover.

My bad. Was looking at newer motor. Your's has the two piece. Check the bolts from the pulley to the harmonic balancer first then the key.