"If the Heroe-ness is partly genetic - then from whom did Hiro and Matt and Niki, etc., get their power?"
They seem to keep changing their mind on how one gets these abilities. In some cases it seems to be hereditary, in others it's a "mutation," and they've also referred to "patient zero," a term used when explaining the spread of a disease.

"Did Niki kill the psychiatrist with the Taser?"
No, the doctor was still twitching on the ground when they took Niki away.

"Why does Peter know that Claude Raines can teach him?"
Peter assumes, because he saw Claude in his vision, that they will be hanging out together. But I also wonder how Peter knows whether Claude is good or evil, helpful or not, etc. As for how he knows Claude's taught others, Claude mentioned this already.

"It's interesting how they never say Mr. Bennet's first name."
I think so, too! I wonder if that would be a big clue as to his real identity or something? In a few weeks, they're going to have the Mr. Bennet "origin" episode, that explains who his partner used to be, how he got Claire, etc. Maybe then we'll find out his name. (I wonder if Claude was his former partner?!)

...Anyway, I found your blog last week looking for people who'd written about Heroes!