Its these kind of questions that made me stop allowing Psionics in my games.
Ultimately the call would be yours
Sure, but if you take any damage while falling, you fall prone.
Forced movement (falling, being bull rushed/dragged/repositioned, and so on) generally does not subtract from your allowed movement in a turn, so you should be able to fall, take falling damage if applicable (and fall prone as a result of that damage), and then full attack. In D&D 3.5, I believe, you could not choose to jump a distance greater than what your speed would normally allow for as part of a move action (and jumping is part of a move action), and I'd be willing to bet it is the same for Pathfinder, so if you jumped before attacking it would take your move action and you couldn't full attack.
Falling = no action
Jumping = move action
I'll chime in with my 2cp's worth on rules.
The player has forced you to start thinking in 3 dimensional combat, this in how I see it: most characters threaten the 3 spaces directly in front of them; the 2 spaces to their left and right; and sense there are no "facing rules" the 3 spaces behind them as well. So you need to take all that space and turn it into a cube of threatened area...ie. a 15ftX15ftX15ft cubic volume. Then should your any of your players space move thru a NPC's space he provokes AoO's as normal, this would mean he would provoke if he moved through the spaces over the NPC's head and the spaces he fell through before he lands on the ground. The provokes as he stands up to fight.
All in all if your player provokes 5 to 6 AoO's by my count then, see if tries that move again.
I would not go 15' up, just 10'. It is really hard to have any affect on something that high. When looking at the two dimensional planes, you are able to move within the center so you never have to reach more than 5' away from an edge. If you go 15' up, you are attacking 9' from and edge (assuming a 6' tall character) all the way up to 12' from an edge (assuming a 3' tall character).
Moving, no matter how much in one round, only provokes one AoO.
I am iffy on geting an AoO for a falling character counting as moving through a square. It happens to fast. If that were the case you would get one on a large creature that goes prone in front of you as they are leaving the second square up (5.1'-10' high). I think this causes to much confusion.
Somewhere I read that the rules only support 2 dimensions, which I don't agree with, but I know I read it.
a) Yes I would agree with Warren, that he provokes AoO when doing that.
b) If he doesn't want to count it for his move action, then it's an uncontrolled fall and he takes full damage from it and most likely ends up prone. No DC 15 acrobatics check either to reduce damage, and no check to avoid AoO by tumbling. You're falling, uncontrolled.
c) If he wants to avoid that he can make a controlled fall and a DC 15 acrobatics check to further reduce the damage. Unless he succeeds on a seperate acrobatics chekc for moving through the enemy squares he also provokes.
Reasoning: Personal Gravity changes gravity for the Psion in such a way that he basicly treats the ceiling as ground, and most likely he stands on his feet up there, hanging with the head down. If he now just switches gravity back into normal... he'll fall head first. To actually prepare for that and land on his feet, he has to prepare, make a handstand for example before changing gravity, or getting ready to land in such a way that he can roll off and stand. That both takes time however.
