The Vader resurrection rumor is from a British tabloid. That alone should tell you how credible it is. And yes, SW has shown that you can clone people's bodies, but there's no indication the personality comes with it. The Clone Troopers in The Clone Wars all have very distinct personalities, rather than being a bunch of Jango Fetts. A clone of Anakin Skywalker would not be Darth Vader, or even Anakin. It would just look and sound like Anakin. Although there was that Dark Horse comic where Palpatine somehow managed to transfer his mind into a clone body, wasn't there?
Yes, Dark Empire (and its sequels, Dark Empire II and Empire's End). He did so via a Force ability, of course.
Well, I imagine it would be centered around a mystery of who's behind the Darth Vader mask now. Vader had become more of a reputation instead of someone who had to make grand displays of power; it would probably take awhile for the average joe to be brave enough to accuse Darth Vader of being an impostor. Disney isn't going to care if it's an Anakin Skywalker under the mask; it's the mask that sells.
There is also the possibility that he might be alive through the immortality technique he learned from Darth Plagueis.