Yeah, I dunno if lie detection is totally passive that it would just fire off whenever someone lies. In any case, I don't think Peter took all of his powers. Peter was bleeding and limping after the confrontation, meaning he didn't regenerate, which he would have been able to do if he had stolen everything Sylar had. Which then makes you wonder how Peter chose shapeshifting, or if he came up with his plan once he figured out what he had.
And no, Quincy, I didn't mean just because he touched the cufflinks. The way Sylar uses his empathy requires him to fully understand his subject. He obtained his electricity power after that 'touching' scene with Elle, after figuring out her major daddy issues and all that jazz. The much of the time where Sylar was hunting the shapeshifter involved him figuring out the shapeshifter's mentality and lifestyle, and he got the power without sawing open James Martin's head. In the case of Nathan, I feel he employed the empathy alongside clairsentience. Clairsentience was allowing Sylar to see defining moments in Nathan's life and from there he could understand all the issues prevalent in Nathan's tale. So I'm pretty sure he was floating due to possessing flight.
Additionally, thinking he was Nathan requires him to think he can fly... heh.