It states on the card that when one of Oracle's agents is given an action, it is allowed to modify one of its combat values +1. Now correct me if I'm wrong but there is 5 kinds of actions; Close Combat, Range Combat, Move, Power, and Free. If I use a Free Action such as Outwit or Perplex, am I allowed to modify my combat values +1 even if I clear the figure?

No. In the DC errata it was changed to disallow free actions.

In other words, whenever (and only in this case) you put a token on an agent, you can apply the +1 to one of the combat values.

Yes. It has to be a token-able action. Same thing if Oracle is on her card (to turn her dial).