Whether it's kitchen appiances, closets, or ceiling heights, I think we see a great deal of the "bigger is better" philosophy when we're talking about home building. I disagree. A higher ceiling may or may not work for any particular space, and raising the ceilings in the entire house somewhat negates the whole point. Read what Sarah Susanka says in her Not So Big House series: She suggests that larger rooms /higher ceilings can feel "out of proportion" to human beings, and they can rob the rooms of the cozy feeling that the owners wanted. She suggests that you consider a change in ceiling or a change in height to denote "spaces within spaces". For example, you might have a higher great room attached to a lower-ceilinged dining area -- that provides a visual cue that this area is different, and it "works" emotionally. Also don't forget to note that higher ceilings do cost more money. Wall materials come in 8' heights; thus, higher ceilings mean more material, more cuts, more labor costs to install. And then they mean more heat /air conditioning later. If budget is important, this is something you can't ignore.

I see no particular problem with the fan being higher. You get less of a direct breeze effect, but it keeps the air moving for a more uniform temperature in the room.

I would go four feet at least. In a room with eight foot ceilings you go down about a foot or so as long as you don't have a particularly tall person clip his hands if he were to stretch. Too high and I don't think you'd get the air flow you want.

Higher is better but put it somewhere you can easily reach to clean the filter. For instance if you have a foldable step ladder figure out how high you can reach on that. If you have to bring in an extension ladder to clean the filter you will be very unhappy.