Originally Posted by DarthJacen
Anakin would win, especially if he caught the Exile alone without her friends from whom she would draw her Force power. And, remember that Anakin's strengths are flying a ship, and seeing things before they happen. He would be so far ahead of the Exile's attacks that she would be forced to defend herself, just, to stay alive. But, the advantage the Exile has is she can, literally, sneak up on Anakin, so if she plans to kill him rather than fight him (because she has no Force signature to give her away she has the same problem the Yuuzhan Vong had.) But, a fight between the two of them would be epic, but I think Anakin will win, simply because he can easily predict what she will do next.
I don't think so. (I despise Vader, so this is biassed)
The Exile's friends are power. Vader/Anakin had no charismatic skills that remotely compared to the Emperor's or the Exile's, so her ability to draw followers to her command is an advantage in itself. The same thing went for Revan, as it was his diplomatic skills that made him so powerful.
She doesn't have a Force signature as you said. Which would mean Anakin would only have had his skills against her and no other precognitive advantage regarding her directly.
I would also say that if the Exile could harness Force lightning, Vader stands no chance at all.