Can you use more then one free action per turn on a character? Say you have Owlman as an agent of the oracle and have the oracle on the card so he gains perplex. Can he then use outwit, perplex and probability (from CSA) all in the same turn?

You betcha. Free actions are just that: Free. Owlman can do all three every turn.

I was going to say just that: free actions are free.

I will add a side note however: do as many free actions per turn as possible. They come in handy.

It's not relevant to the answers provided, but I thought I should point out that Probability Control is not an action, free or otherwise.

I would also like to add that Probability Control is not an action. It just happens.
That's why you can use it on your opponent's turn.

Just to clarify; you can only use PC once per round during your opponent’s turn, right??

I always seems to get this wrong, so if you could clarify, I'd appreciate it...

Right. Or, in multi-player games, once when it is not your turn - if you use your PC to make opponent #1 reroll, you cannot force opponent #2 to reroll that same round.