What is the best place to install an Air-conditioner in a room?
In order of questions asked:


It is best to install the indoor unit near the area of maximum heat loss and gain.  Above a window is a fine place, provided you have space to run the refrigerant piping and condensate line.
Near a corner is okay, but a less central location means there will be a longer time required to circulate air around the room.
As a licensed refrigeration person I can say that outdoor installations near the ground are usually more pleasant to service than those that are on a roof.  Most modern mini splits are very quiet.  As long as the outdoor unit is not directly next to a window, you probably will not be bothered by the noise.
Outdoor unit installed above or below the indoor unit does not matter as long as the total lift and length of piping is within the manufacturer specifications.