1) The order essentially doesn't matter. You're over-thinking this. The general advice though the ages is to put what you're interested in the middle, and start (and end) on things you aren't interested in.
2) The only way this might matter is for personal reasons, i.e. your wife giving birth, as you may want to avoid the more brutal rotations. Surgery (and inpatient OBGYN) are busier than IM and Peds, which are busier than FM and psych. Alternatively, you could think in terms of how hard the shelf exams are: this is subjective and may have changed since I was a med student, but I think it was generally agreed, in terms of difficulty (i.e. the volume of material, not the amount of time you have to study), FM (by far the hardest shelf) > peds > IM = surgery > obgyn > psych.
3) Your school spends 2 months each on FM and psych? Seems like a lot.