
Quintain |

You threaten every square in which you can make a melee attack. So, with a regular reach of 5', that's every square adjacent to you (including your own square); 9 squares in a 3x3 pattern. Add a 3D element to the board, that includes the squares above you too; 9 squares stacked on 9 squares.Dropping from above, you have to enter one of those upper 9 squares to make a melee attack on your opponent.
The question is, can you make an attack while in midair? What about a charge attack in midair?
You want to stop moving in a square above your target to make an attack, but can you? You say, this square (in midair) is where I stop moving. But, you start falling then. Do you postpone falling so you can make an attack?
And if you fall out of a threatened square, does an attack of opportunity happen?
Now, I'm all for cool stuff happening in the game and letting certain rules slide for coolness...
But since this is a rules forum:
By RAW, can you make an attack in midair before you fall?
By RAW, does an opponent get an attack of opportunity if you fall out of their threatened square?
Well, if you enter one of the opponent's threatened squares (and we are talking about the ones that are on the higher level diagonal. You would enter them and make the attack.
Under standard charging rules, given a flat plane, you would then stop because you are in control over your own movement.
Since, you are jumping down, and the "down" part is essentially uncontrolled, the rules of physics would take over. You would enter the threatened square, make your attack and then essentially fall. If your opponent were tall enough, you could take damage, and incur a attack of opportunity by "moving vertically" through threatened squares.
Thus, doing a "jump-charge" from an adjacent square would, imo, provoke 2 attacks of opportunity, one from the upward vertical movement, and a second from the downward vertical movement.

Quandary |

right, assuming you attack from the upper diagonal square (or, the first threatened square you enter, jumping/falling from above), your attack resolves first and then 'gravity happens' afterwards, provoking an AoO for leaving a square. not much different than if an enemy is flying just out of reach off a cliff, you decide to 5' step off the cliff (putting you in range of the enemy), you attack them, and then gravity happens/you fall. i count falling movement towards a characters' movement, so you can't fall more than a certain distance and still have an action remaining, but falling can also EXCEED your movement speed, by that point you wouldn't have any actions remaining though (i would even exclude swift and most free actions, your turn basically ends and the rest of the falling movement happens for that round).