If I Outwit someone's power, and my Outwit is Outwitted by an opponent... but then a third player KO's that opponent's Outwitter and I get my Outwit back, am I still Outwitting the original target? Or does the Outwit power have "no memory" when it returns?

I am perplexed

The original target is not Outwitted. The only time Outwit has a "memory" is if, in one attack, you get clicked from Outwit back onto it. (Basically the character never lost it).

You can only use Outwit on your turn
Your Outwit is cancelled during someone else's turn

And as far as you being Perplexed, I believe the rules state that Perplex is against enemy figures, not the other player (I have a coupon for 20% off my opponent's IQ!)