The levitation or speed I think is really just telekinesis, which is also how he does the skull-splitting. He just refined telekinesis to be an invisible weapon, forklift, whatever. It's like he's the Green Lantern only his ring powers are invisible. Also, he has no ring.

But you've got me on the Walker thing. It's possible that that's not where he got the ice powers. Otherwise, the show's been pretty good about not letting him develop powers out of nowhere that we wouldn't understand how he'd gotten them.

Except for the one that lets him rise from the dead, apparently, because the doctor at Bennet's organization definitely had a corpse on his hands (and, presuming he was a competant enough doctor--he was trusted with Sylar's containment and life, so I assume he was--he would be able to tell the difference if Sylar weren't actually dead).