Here's my take on things:
First, yeah, it's a mess. A real disappointment. Having gotten that out of the way...
Elle, in the wake of her catharsis from Syler deconstructing her with his empathy (nngh), has become a rogue agent. No longer beholden to the Company, nor Pinehurst, she's decided that she, and Sylar, can do whatever they want...so why not do it? This is the agenda she pushes on Sylar...who continues to be ridiculously easily manipulated in this entire season. This is one of the many, many examples of weak, lazy writing in Season 3. Whenever they need Sylar to switch sides, they just have someone say a paragraph or so, and bam. Done. Swapped. He's done it THREE times now.
Sylar knew where Claire was because he's "analyzed" HRG's brainz0rs from when HRG and he were trading barbs. We've sort of seen this from Sylar before...it's not psychic so much as just having a quick ability to gauge a person's inner workings. Of course, I'm not sure how this would give him access to one of the -many dozens of places- HRG could have taken Claire. Especially when Sylar didn't even KNOW Claire had gone after Black Hole Man, and had no way of knowing that. Weak and lazy writing.
The theory of the eclipse seems to be: the powers started with an eclipse, and an eclipse can turn them off too. Why? Eh. I get a definite feeling that they're trying for a Hail Mary here...a sort of Crisis on Infinite Earths resolution to all of the innumerable continuity problems that their overuse of time travel, inconsistant pseudoscience, and the fiasco of Season 2 left them with. Reset to start positions. No one has powers again. Claire's good again. Sylar's bad again. Take it from the top, people.
It's gimmicky, and silly, but if it puts an end to the madness and lets them have a stab at recapturing what made the show great in the first place, I'll be fine with it. Everything now rests on what they do next.
My prediction is that when the eclipse is over, powers will return. Most likely gradually...though possibly with dramatic speed. Alternatively, Hiro will do something (the "I have a plan" clause) like bend time to make another eclipse that turns powers back on.
Sorta like The Clapper. Eclipse on! Eclipse off!
They'll be reset though. So Vampire Dad will have to start over. Peter will start over. Sylar will start over. Of course, with Peter that's not much of a burden...it is possible (though unlikely) that they'll find some other way to neuter him, up to and including killing him during the eclipse or before he absorbs Claire again.
I think Sylar will wind up killing Dad and taking his stuff.
I think Nathan will finally go public with superpowers, and this time Peter will either let it happen, or he'll be dead so he can't come back AGAIN. Then next season, if there is one, will be about the public reaction to superpeople, and the possibility of the show's mythology progressing onto things like supergroups, laws for powers, tension between normal people and superpeople...maybe even a cult of celebrity for supers and what that means.
Could be neat. If it was done well. Which I don't have high hopes for.