Can a character with Outwit use it as a free action and then make a power action to "Thwart" a feat card in the same turn?

As far as I'm concerned, it seems valid, yes.
As you said, you give your character a free action to use Outwit, and then a power action to use Thwart: seems good to me (you only gave 1 non-free action to your character), and I didn't find anything in the FAQ and/or in the E&C that prevents it.

Use a power action to Thwart the Feat (Fort) and then Outwit Impervious.

YES V docter doom will never be totally safe anymore i can finally thwart fortitude then outwit mastermind! doom is goin down now!

Assuming he doesn't Wildcard Batman/Kabuki, yes.

Otherwise, you're still not going be able to draw LOF to Outwit him

Doom does not go down... Doom is just lulling you into a false sense of security. Doom will strike when you least expect it!

Yes, my judge used it on me at tonight's tournament! Nerfed my gorilla's TK, then thwarted my Spidey's Pounce. I was royally cheesed off.

Then I took my Allen the Alien and busted up his V Mr. Terrific with aplomb.

Let me tell you something, he ain't that terrific. It was a good thing I had that plomb handy.

What if its a wildcard itself doing the outwitting, Like a Nightthrasher or Brainiac 13 copying Ultimates or Sup ally..

Doom Goes down!!! LOL But it takes a lot of work.

And assuming Doom doesn't Thwart your Thwart first, of course - he has Mastermind, so he can use it on his top click.