How is this scenario supposed to play out?
Human Fighter with Greater Bull Rush and Bull Rush Strike takes a 15ft Move Action towards an enemy and uses a Standard Action to make an Attack Action and causes damage and his turn is over. The enemy takes his turn to move around the Fighter towards one of his allies. This provokes an Attack of Opportunity from the Fighter. The Fighter critically strikes and confirms, and decides to Bull Rush using Bull Rush Strike and defeats the CMD by 10, so the enemy is moved 15 feet. The Fighter still had enough Movement left, and was allowed to follow the enemy during this 15 foot Bull Rush. The enemy had 40 ft move speed, and already moved 5 feet, which provoked, and then was moved 15 feet by the Bull Rush.
Does the enemy now have the ability to use the remaining 20 ft of his movement? And would this movement would provoke again?
The bull rush attack of opportunity doesn't prevent the opponent from continuing their movement after the AOO. If the opponent had been tripped, then he would have to use a move action to stand, which would break his original movement action.
I don't see why your adding the bull rush movement to the opponents total movement for the action. The bull rush movement is imposed on the opponent, it isn't part of his movement, so he should still have 35 movement if his base movement is 40.
For you last question look in the section Combat- Attacks of Opportunity - Combat Reflexes and Additional Attacks of Opportunity, you will find the line "Moving out of more than one square threatened by the same opponent in the same round doesn't count as more than one opportunity for that opponent." I played under a GM back when we didn't notice this rule (probably because we came from AD&D 3.0) and fighting an Elder Fire Elemental end up being very painful for the rogue trying to flank.
Cool, ty ;)