Stand Still only works with enemies who are adjacent
When a foe provokes an attack of opportunity due to moving through your adjacent squares, you can make a combat maneuver check as your attack of opportunity. If successful, the enemy cannot move for the rest of his turn. An enemy can still take the rest of his action, but cannot move. This feat also applies to any creature that attempts to move from a square that is adjacent to you if such movement provokes an attack of opportunity.
What I want to know is whether I can move and position myself in a way that the next 5ft movement triggers Stand Still
No, for example, if you were large with 10ft natural reach, you wouldn't get to stand still someone who is 10ft away from you. The same applies even if your effective threaten area is further than adjacent only. Even if they move through a threaten square in the area of the expanded combat patrol, it isn't an adjacent square when you choose to move as part of the AoO, so it still wouldn't qualify as an adjacent square to complete the AoO just because you moved adjacent to it.
Still wouldn't work (100% of the time), because the provoking creature didn't provoke from you but the animal. That said, technically movement is incremental, so if they continued moving and provoked again by now leaving a square threatened by the guy on the mount, it could work. But that could then be circumvented by going into acrobatics to roll and rolling (pun intended) well, the specifics of the rider's reach, etc.
That wouldn't work because you wouldn't be able to resolve the AoO as the target isn't within your threaten range (meaning you can't respond to it, even though the mount will then move after the opportunity passes), and still didn't technically mean they passed through *your* adjacent square.
Paired opportunist doesn't also multiply the provoking by the number of allies with the feat threatening the same guy who provokes, it just lets more people capitalize one the same incident that normally wouldn't: e.g. guy attempts a maneuver on someone with PO, and the other guy he didn't try to maneuver (who also has PO) also gets to join in on the AoO provoke.
This is how I read the Paired Opportunist/Combat Patrol/Stand Still situation. Please, correct me if I'm wrong:
Benefit: Whenever you are adjacent to an ally who also has this feat, you receive a +4 circumstance bonus on attacks of opportunity against creatures that you both threaten.
Enemies that provoke attacks of opportunity from your ally also provoke attacks of opportunity from you so long as you threaten them (even if the situation or an ability would normally deny you the attack of opportunity).
This does not allow you to take more than one attack of opportunity against a creature for a given action.
Benefit: As a full-round action, you may set up a combat patrol, increasing your threatened area by 5 feet for every 5 points of your base attack bonus.
Until the beginning of your next turn, you may make attacks of opportunity against any opponent in this threatened area that provokes attacks of opportunity.
You may move as part of these attacks, provided your total movement before your next turn does not exceed your speed. Any movement you make provokes attacks of opportunity as normal.
Benefit: When a foe provokes an attack of opportunity due to moving through your adjacent squares, you can make a combat maneuver check as your attack of opportunity. If successful, the enemy cannot move for the rest of his turn.
An enemy can still take the rest of his action, but cannot move. This feat also applies to any creature that attempts to move from a square that is adjacent to you if such movement provokes an attack of opportunity.
If two allies are both threatening the same creature and are adjacent to each other then an adjacent foe moving through adjacent squares will make proc Stand Still from AllyA and Paired Opportunist from AllyB.
If a foe provokes an attack of opportunity while being in the Combat Patrol's threatened area the patrolling creature would be able to move as a part of the attack, if by doing so both AllyA and AllyB would still both threaten the same creature and be adjacent to each other it'll proc Paired Opportunist from the ally wich isn't patrolling.
Foe (moving trough adacent squares) > AllyA (Stand Still) > AllyB (Paired Opportunists)
Foe (provoking any attack of opportunity) > AllyB (Combat Patrol) > AllyA (Paired Opporunists)
An action would make Paired Opportunist proc against an enemy just once though.
For AllyB to benefit from paired opportunists in scenario 1, he needs to not already be able to capitalize on the provoke from movement normally, which if he's already threatening the foe, he already is getting to act on the provoke. Paired Opportunists isn't an extra provoke for other allies for whenever you *act* on the provoke, it's just granting other allies the ability to join in if they couldn't already.
Another example might be AllyA has Outflank and Paired Opportunist, AllyB just has Outflank, and AllyC has Paired Opportunist: If AllyB crits a foe that is (Out)flanked with AllyA, AllyC wouldn't normally get to join in AllyA on that provoke (even if he also is technically flanking as well), but Paired Opportunist does. There's also just a rogue with the Opportunist Advanced Rogue Talent with PO just sharing the Opportunist AoO with everyone who also has PO, what was probably the namesake/most expected use of the ability.
For scenario 2, I still disagree as I believe that for a combat patrol mount to be allowed to move you into range to have capitalized on the AoO, the window of the actual provoking has passed. Basically yes, for logistical reasons the players won't all immediately and at the same time throw their dice at the GM as soon as a foe provokes, but will do so in some level of order of declaration, but they all decide if they can/will act on the provoke at the same step of the action, and then once it all starts to resolve, that step has passed. So even if what the mount decides to do for the provoke brings you to the foe, that doesn't override the fact that the rider couldn't have chose to act on the AoO from his position when it happened, regardless of PO or not.
(That said, because mounted combat rules are all sorts of borked, I'd personally allow a rider who had Combat Patrol in parallel with the mount to be able to act on the AoO when the mount arrives, even without PO and though obviously the rider isn't technically the one doing the moving, the mount is.)