1. The fan is above the desk.

(Can we use 'above' any time when the fan is on the ceiling, for example, in each corner. When the fan is directly over the desk, can we use "over" as in the sentence? Can we use 'above' when the fan is in each corner of the ceiling.)

2. The fan is over the desk.
(Do we use 'over' when the fan is directly above the desk verticallty? When the fan is in each corner, can't we use 'over? If the desk is in the midder of the room, the fan is not directly above the desk.)

If the fan is sitting on one corner of the desk or the other corner, you'd say the fan is ON the desk.

http://i.ebayimg.com/00/s/NDM2WDI2Nw==/z/EisAAMXQVERSsTH0/$_35.JPG?set_id=2

To be ABOVE the desk or OVER the desk, it would have to be mounted on the wall and above the surface of the desk or suspended from the ceiling.

1. Yes, you can use 'above' to describe the fan's position when it is on the ceiling in each corner. 'Above' implies a position that is higher or elevated compared to the object it is referring to. So, if the fan is in each corner of the ceiling, you can say "The fan is above the desk."

However, it's important to note that when the fan is directly positioned over the desk, it's more accurate to use the word 'over' to describe its position. 'Over' implies a position that is directly on top or directly above the object. So, if the fan is directly above the desk, you can say "The fan is over the desk."

2. Yes, 'over' is commonly used when the fan is directly above the desk, vertically or horizontally. If the fan is in each corner, you can still use 'over' to describe its position, as long as it is directly above the desk, even if it's not positioned in the center.

For example, if the fan is in one corner of the ceiling and directly above the desk, you can say "The fan is over the desk." However, if the fan is in the corner but not directly above the desk, it would be more accurate to use 'above' and say "The fan is above the desk."

Remember that the choice between using 'over' or 'above' depends on the specific position and relationship between the fan and the desk.