The question about running the fan in the pull air up or push air down mode is more tied to whether or not you want to feel the air moving on your skin than any laws of thermodynamics. When the fan is pushing down, the air column comes down under the fan, where you are more likely to be. When the fan is pulling up, the air flows down the walls, where you are less likely to be. Also, as the wall perimeter is typically greater than the diameter of the air column, the sensation on your skin is less, even if you are standing against the wall.
I went with depends on the temperature but the reality is it depends on which way the fan is set. I haven't changed them since we moved in but they do run summer and winter unless we close the house up when gone for a while. Movement is movement and helps. We don't site directly under any of them so I don't care which way that movement is going.