Combat Challenge and Combat Superiority do not combine as Combat Challenge is not an OA it is specifically a "Melee Basic Attack". Feats that add to OA do not improve CC for the same reason.
A fighter's Opportunity Attack stops a creature on a hit, and it can move no further as part of that action. If the creature still has unspent actions which could be used for movement, it can spend them to move on, and the fighter cannot attack it again, since he's already used an Opportunity Action on its turn.
Note that the fighter's Immediate Interrupt attack against an adjacent marked opponent which shifts or attacks another target is not an Opportunity Attack. He neither gains his Wisdom bonus to the attack nor stops the target's movement if he hits.
Does he get both, our DM is only letting the fighter get one as he says the fighter can have only 1 OA
As for making an OA on your turn, you can't ...
But some circumstances or powers would make it possible if the rules allow it.
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Or if a monster readied a charge on your turn, and charges past you.
If a monster triggers and action on your turn, does the monster make it temporarily itw own turn, which would make it not your turn and thus allow the OA?
As mentioned, Combat Challenge is NOT an Opportunity Attack, it is an Immediate Action, which is a completely separate category of out-of-turn actions.
So, for instance, if a marked opponent next to the fighter makes a ranged attack against another character, the fighter can make both an Opportunity Attack and a Combat Challenge attack against him, in either order.
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However, note that any character can have only one Immediate Action per round. If one opponent triggers the fighter's Combat Challenge attack (or if he uses any other form of Immediate Action), he cannot then use that attack when subsequently triggered until it refreshes on his next turn.
Combat Challenge and Opportunity Attacks are both immediate actions (one is an interrupt and the other is a reaction).