1. If the monk doesn't have improved trip, can the baddie make an AoO in reaction to the monk's AoO trip? If the Baddies doesn't have improved trip, can the monk? Can this create an infinite loop?
It can happen but it does not go infinite; there is a limit on how many attacks of opportunity one can do in a round.
2. If successful, does the trip happen before or after the baddie moves? If before, does the baddie lose any movement spaces he had left in that move action? If not, could he choose to use the remaining movement spaces to crawl?
Attacks of opportunity interrupt the triggering action. If this makes the action impossible, the action is wasted. The person whose turn it is can decide if they want to do something else with their remaining actions.
3. Can the baddie use his standard action and attempt the same movement?
Yes, though if he was knocked prone, he might need an ability to get up from prone as swift or free.
4. If he chooses to do the above, does this count as the same action or a different action for provoking AoO?
It is a different action. If you have attacks of opportunity remaining, you may try to trip him again.
2. If successful, does the trip happen before or after the baddie moves? If before, does the baddie lose any movement spaces he had left in that move action? If not, could he choose to use the remaining movement spaces to crawl?
I would say that it interrupts the action. The baddie would be knocked prone on the field where the AoO happened (or maybe 1 field further, depending on his move speed and a coin toss, let him fly in a high arc). An indication to this is actually the ruling regarding casting spells and executing combat maneuvers: in both cases, one has to take the damage from the attack of opportunity (if any) as penalty to the concentration- or CMB-check.
3. Can the baddie use his standard action and attempt the same movement?
4. If he chooses to do the above, does this count as the same action or a different action for provoking AoO?
Yes, he can. He will still provoke AoO's. You only say "I want to use my standard action to execute a (second) move action". This does not alter any properties of the move action. Withdraw lets you move out an threatened area without (certain) provoking AoO's, and it is a full-round action.
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Let's try it this way...
PC A and PC B both have the Paired Opportunist feat... which allows you to get an AoO if an ally of yours who also has the feat does.
NPC C does something which grants A an AoO. B therefore ALSO gets an AoO on C because of Paired Opportunist. However, A does not then get ANOTHER AoO on C based on B's AoO... it does not loop. A & B each get only one AoO for the initial triggering action C performed.
There are not just no INFINITE loops... but no loops at all. Once you get back to any character getting a second AoO derived from a single triggering action you stop... one AoO per trigger action.
I didn't think that one could perform a combat maneuver as an attack of opportunity.
Making an Attack of Opportunity: An attack of opportunity is a single melee attack, and most characters can only make one per round. You don't have to make an attack of opportunity if you don't want to. You make your attack of opportunity at your normal attack bonus, even if you've already attacked in the round.
An attack of opportunity is defined here as a single melee attack, which isn't a combat maneuver. The only way something could get a chance to trip on an attack of opportunity is if it had the Trip monster ability that causes its standard melee attacks to also result in a trip attempt.
I didn't think that one could perform a combat maneuver as an attack of opportunity.
Making an Attack of Opportunity: An attack of opportunity is a single melee attack, and most characters can only make one per round. You don't have to make an attack of opportunity if you don't want to. You make your attack of opportunity at your normal attack bonus, even if you've already attacked in the round.An attack of opportunity is defined here as a single melee attack, which isn't a combat maneuver. The only way something could get a chance to trip on an attack of opportunity is if it had the Trip monster ability that causes its standard melee attacks to also result in a trip attempt.
And some combat maneuvers replace a melee attack. Like trip or disarm.
Performing a Combat Maneuver: When performing a combat maneuver, you must use an action appropriate to the maneuver you are attempting to perform. While many combat maneuvers can be performed as part of an attack action, full-attack action, or attack of opportunity (in place of a melee attack), others require a specific action.
You can attempt to trip your opponent in place of a melee attack. You can only trip an opponent who is no more than one size category larger than you. If you do not have the Improved Trip feat, or a similar ability, initiating a trip provokes an attack of opportunity from the target of your maneuver.
Congrats on asking one of the hotly debated questions.
Your trip goes off before they move.
1) they chose move action move, and are locked into that choice so a successful trip cancels their move action. Since crawling is a different action than move they can't swap to it. They must use another action to crawl.
2) they are allowed takebacksies and can do a different move action since they "never really got to do their move action" so yes you're allowed to change that move action move which provoked into a move action crawl, but the crawl still provokes as normal.
It's not worth discussing beyond this. (please don't have the thread be hijacked by this topic). Just know there are two groups, both large, both currently allowed to be correct, ask your GM which is being used.