“So all the time travel actually makes sense when you view it from the perspective of like a tree with a main trunk and many branches.

That's as logical an answer as I could arrive at, per my earlier comment. It seems like a lot to expect from the typical TV viewing audience, though.

Peter absorbs Jessica's "extra strength"

Ah! I hadn't picked up on that. Thanks!

To answer some of your questions, here is my take:

1. Many of your questions with time travel seem to assume a singular linear timeline. This is not the case. Most science fiction works, including Heroes, that involve time travel postulate multiple alternate timelines that all diverge off from the "main timeline." In Heroes, the "main" timeline is the first future experienced by Hiro: Sylar kills Claire and absorbs her power; Hiro stabs Sylar; Sylar regenerates; Sylar explodes.

The first divergence from this timeline (or second timeline) occurs when Hiro goes to the future the second time (Heroes are terrorists; sylar is nathan, etc.). In this timeline, Hiro sucessfully goes back in time to warn Peter to save Claire; Peter saves claire and Sylar does not absord her powers; Claire lives and becomes a waitress; Peter–not sylar–turns into the atomic bomb in this one. However, Nathan does not rescue Peter, allows him to explode and follows Lindemann's plans for a "better future".

Finally, the "third" timeline (or the second divergence from the main timeline) occurs after Hiro returns from the future the second time. In this timeline—which is what we see as the "present" in the series—Hiro returns from evil future and warns Nathan that he will become president after the bomb but will become a very evil man. Peter has already saved claire so sylar doesn't absorb his powers; Hiro is able to kill Slyar; Peter explodes; Nathan decides to rescue Peter and fly him away based on Hiro's warning about him becoming a villian and Claire's pleas to change the future.

–So all the time travel actually makes sense when you view it from the perspective of like a tree with a main trunk and many branches.

2. Why was Hiro able to kill Sylar so easily. Sylar did not have Claire's power of regeneration and just took an a$$ whooping by Jessica and Peter. Jessica smacks him in the face with a parking meter while standing next to Peter; Peter absorbs Jessica's "extra strength" and gives Sylar a good ol' wholloping–If you listen to the soundtrack closely the same sound effects for Jessica's superpunches are used when Peter goes fisticuffs with Sylar.

3. The tough questions for me is why did Peter explode; did he absorb too many powers and couldn't control them all? Not likely, being in close proximity to sylar, he must have assumed sylar's ability to quickly control his new powers. My best explanation is based on Charles' comments to Mrs. Petrelli about how emotional Peter is and Peter's revelation to the invisible man that he can only use a given power when thinking about the person who gave it to him. Given the level of emotions running at the climax, it is easy to see why he would explode. Alternative explanation is that after the death of Simone, Peter "lost his ability to love" and thus lost control over his powers

Right now, the only explanation I can think of for the first season's conclusion is alternate timelines or parallel universes. That'd also explain Isaac's fallible paintings (the bomb, the Oval Office). But what did he mean when he said, "Now I've shown them how to stop the bomb — and how to kill you [Sylar]"? All I saw he did was draw a picture of Hiro impaling Sylar, which wasn't very helpful; nor did it address the bomb issue…

Firstly, some your of questions are based on things you only think you know! ;-)

Secondly, about Mohinder: I keep adding up 2 (his sister had the disease, implying she was empowered) and 2 (there seems to be a strong genetic link), and getting 4 (Mohinder will turn out to have an as-yet-unknown power).

After all the training Hiro received from Sulu

I wish I could berate you for calling him "Sulu", but that would make me a hypocrite! (Talk about type cast…)