If wind rotates my fan, will it cause electrical problems?
It is quite likely that the motor of your fan is an induction motor. Except if this kind of device is connected to a capacitor, it won't generate noticeable voltage even if something external makes it spin.

If this fan is a little more complicated and includes a rectifier and a DC brushless motor, there can be some voltage generated if the rotor spins, and the rotating magnets create some electromotive force in the windings. But, even in that case:


the voltage will be blocked by the rectifier, and you won't see anything between the terminals;
the electronics could be damaged only if the rotation speed exceeds the normal rated one, which I think is unlikely


As a conclusion, I don't think a rotation could directly damage your fan or external circuitry.

Maybe the highest hazard could come from the fan rotating (rapidly) in reverse when the circuit is switched on. In that particular case, the start torque and initial current could be a little higher than the normal ones.