As to why Mohinder didn't just shoot Sylar when he knocked him out, they had to make a lot of changes to the episode and some were made a day before shooting began.
http://gregbeeman.blogspot.com/There were also more beats of action in the Sylar/Peter fight, including that Sylar was pushed out a window by Suresh and fell several stories to the pavement.
So in the original script, Mohinder wouldn't have even been in a position to shoot Sylar at all and it was probably something the writers didn't even think of when the change was made.
Simone's father was probably involved in the company, his building was in the flashback with BennetDad and Hiro's Dad and it seems to be an important focal point.
Peter has been in the same room as Parkman, they both read each other's minds and caused a headache of feedback.
Peter's powers seem to be a combination of active and passive uses. It's mostly passive when he's around the original user and especially if that person is using theirs at the time. Claire, Claude, Parkman, and Nathan were all using theirs around him and he picked them up and used them easily and right away.
After that, he's been passive when not around the person or when they're not using their powers around him. TK, healing, and flying all happened without his conscious thought about them.
He can activate them consciously, he seems to have mastered invisibility at least.
But there's almost no information about his base power. He may need to be in contact with someone for a certain length of time if they aren't using their power, if length of time is important does he automatically retain them if the person was using theirs around him, do some powers take importance over others depending on these factors, he may need to 'recharge' after a certain period, he may gain them indefinitely if he's been around a person like a family member long enough, he may only be borrowing them and if they die it's gone, and so on.
How his base power works is important to determining what other powers he may have. He could have passed people on the street who were powered without his knowledge.
But the one power I want them to explore, and one that he almost certainly has, is Hiro's.













