How does Sylar find the heroes? Maybe one of his powers is locating who is like him? The smart/memory woman he killed said she has just started remembering things reall well recently and all the sudden she dies. To me that power seemed like the most normal, I mean there are people like that in today's real society. Doesn't seem too "Heroes" worthy, but I guess maybe he got rid of her to obtain her ability.

I do not believe that Sylar kills heroes to get their powers. I think he kills them just to kill them.. Wasn't there that big God Forgive Me thing painted on the wall of his NY apartment? I think he's a serial killer and he believes he's doing god's work by ridding the world of this evil. But hey I could be wrong.

And he finds them because he had a copy of Chandra's map in his apartment and it was more complete than Chandra's.. You know the map with all the string and pictures?

Does seem a shame to kill a girl that was basically a living "google", but in Sylar's mind she was evil. he wants to kill them all.

I don't remember who it was, but someone suggested that Sylar is killing others with abilities in order to be the only person on earth with powers. Thus, elevating him to a god like status.

It seemed to me that Sylar was in the diner because he was preparing to go for Jackie (not Claire, because she is not in the newspaper) and he just happened to notice that she is special and making references about "6 months ago". Then and there he decided to kill her. I think?

I don't think he can sense heroes.

I think he is only following the map. He met face to face with Matt and didn't kill him either, and he couldn't sense Molly hiding under the stairs.

He also left Hiro alive in the diner, even though he would have been alone in the bathroom at the time. If he could sense powers, he would have taken Hiro first. The reason he was there for Charlie is that her picture is on his map just above Claire's.

Can you please tell me where to find a picture of Claire on a map? And then Charlie, please.
I haven't seen any of this?

So...if he thinks he's doing "God's Work" by killing all superhumans...wouldn't he, eventually, kill himself as well?

In the spoiler section. Pictures for episode 10.
(I think that picture you are referring to is one of those non-canon shots we should take with a pinch of salt. But its a nice photo all the same.)

Absolutely. But first he has to kill all the other superhumans to make sure the genes don't propagate. So it doesn't really matter, as by the time he would all of the main characters of the show would be gone and it would suck.

If the research shows powers, his primary target would be claire, but on route it would be nice to pick up memory power on the way assuming that he is collecting powers.

if not then they are still nearby each other, short trip to kill 2 heroes.

Maybe becuase wher powerspif she had any[ would have developed more and more, and he woul rather just eat her brain now then wait until she gets powerful or something

I really don't think he eats the brains. Nor does he Absorb their powers. I have yet to see him demonstrate any power other than TK.

I'm pretty sure it was the little girl who could freeze.
TK covers the bullets, the jumping, and the instances of objects used as weapons.

about him ripping out peoples brains, he may be ripping out the brains so that if he does kill claire he knows that she will stay dead. he may not kno who she is, just that she can regenerate. he also seems to just be killing girls mostly. He may be looking for claire but not kno exctly where or who she is.