HDMe2 unfortunately that's the sorta thing that's made this show such a wreck, but thankfully that's not what happened. Claire, Noah, and Peter talked to the guards, then they made the switch and put Peter in as the President. The fact that they didn't show what happened to the other guy Sylar replaced was probably just prudent editing.
As far as Peter's powers go, it's possible that Peter just took the one ability, but here's the question: Can Peter do what his father did? Their powers seem very similar, but Pappa was able to take someone's power completely leaving them powerless. When he took Peter's ability, he seemed to take them all. Peter may not be able to that, take on multiple abilities from one person, or maybe he just didn't get enough contact with Sylar during the fight...Sylar probably figured out what Peter was up to before he was able to absorb all of his abilities, and that's why he took the fight away from Peter.
I don't know, but honestly I've never had a problem with Peter's super ability, or Hiro's, or even Sylar's--the problem has always been the writing--making the characters act, behave, and respond in ways that makes sense. Like seriously, Claire's blood should've been used to save Nathan...in fact everyone should be carrying a vile of it around for just such emergencies LOL