When some windows are open, the incoming wind spins my ceiling fan. Will this damage the fan? (bonus points for a gadget that makes it power my house)
No. It can free spin and not be damaged and it is unlikely the wind will spin it faster than it is designed for.
Only if it is running and the wind is slowing it down, it might cause the motor to heat up beyond what it was intended for.
It is a very low spin. It gives that bad guys’ den look to my living room (which does little to offset the books and the wooden fruit)
For whatever it’s worth I’ve got one in the covered walkway that goes from my house to garage that has experienced everything from a near constant breeze to hurricanes during the last seven or eight years it’s been in place. It still works perfectly fine, so if that’s any indication the effects would be either absent or negligible to the point of being immaterial.