The questions were:
The fan uses electricity. By the Second Law of Thermodynamics, this electricity is converted into heat. So, the fan generates a small amount of heat, which warms the air in the room. However, this is so small that the third answer is also acceptable.
Of course, in the days of the Indian Raj, the equivalent device was the punkah, worked by a punkah wallah. Same applies: the poor fellow's work generated heat, but probably not enough to noticeably warm the room. Anyway, as the picture shows, he had to sit out in the sun. This was the major cause of the "Sepoy rebellion."
True. The air cools by causing sweat to evaporate. If your body is not in the direct path of the airflow, the fan is doing nothing but using up electricity.
If you don't believe me, try an experiment. Have a floor fan on high, and sit behind it.
True. There are several such situations:
When the fan is not turned on.
When the humidity of the air is high, so an airflow does not result in evaporation.
When there is no one in the room.
When a person's skin is covered in clothing that interferes with the evaporation of sweat.
When you are feeling cold anyway and would prefer to warm up.
PLEASE do not throw your fan at me!