The fan is thermostatically controlled, and will only spin as fast as is needed to keep the engine cool. If you can spin it by hand, and there is no resistance, and it continues to spin freely, the thermal unit is bad, and needs to be replaced. The other extreme is that the thermal unit locks up, and the fan spins with engine speed.
A little more explanation of the changes in idle would be helpful. Some idle variation may be normal.
shady