The fan will move with much higher angular frequency as there is no air resistance. And the angular frequency will be increasing till the blades of the fan breaks.
You switch on a fan in space.motor rotates, blade rotates- no air. After some time to your surprise still no air. But the magical part is when the motor heats up and there is nothing around where it can dissipate the heat energy, so the motor coil inside it burns out. Motor stops and to your surprise still no air.
Nothing really! The fan moves due to a motor, the motor will get overheated in the absence of air as dissipation, unless u r doing something else to cool the motor! If the fan is not fixed on something large, the blades would rotate in one direction while the body in the opposite direction.