IIRC he hasn't made an appearance in the text since Winter's Heart when he was in Far Madding.

So it begs the question where has he gotten off too? How has the Cleansing/destruction of Mashadar affected him? Have his mystery powers grown or perhaps depleted? What is his ultimate role in the series?

As for where I think he is: I think he'll next appear back with the Seanchan, he's always managed to wriggle his way onto the side of Rand's biggest opponents during the series, and at the moment that would be Tuon. He could even be the one to discover Elaida and tell the Seanchan who she was.

What affect did the Cleansing have on him: I'm certain he's aware of it on some level, but I doubt it did much unless it increased the intensity of his brand of evil since he is now all that is left.

Powers: I bet they've grown considerably during his hiatus, he seems to have new abilities every time we see him.

Ultimate role in the series: Have have 2 thoughts, one is "out there" and one is boring...

1. I think Padan Fain will somehow help to destroy the DO and in so doing with rise up as the "new evil" that Rand will seal away outside of the Pattern. It's possible that S'T was also once just a man who discovered, and carried, all the world's evil and was sealed outside of the pattern in a distant past by the Dragon of that Age.

2. Alternatively Fain may just end up dying an uneventful death during the LB while trying to kill Rand. I certainly hope not since he's been built up to be some kind of mega-baddy!