Why exactly do you think Tim Kaine would help in North Carolina 2012? Because he’s from Virginia? Didn’t exactly help Hillary, did it? I suppose if he doesn’t push the campaign to endorse gay marriage like Biden did, it might help a bit in NC that year. But ultimately I doubt it makes any notable difference. Definitely he doesn’t do as well in the VP debates as Biden did. 2008 he probably wins anyway because Palin was so awful, but 2012 is another story.
More interesting are the implications down the line: Hillary doesn’t choose Kaine as VP. Maybe she chooses someone who would help her more like Sherrod Brown. And Biden would not be the nominee right now either way. He would probably still be in the Senate.
This is true. But I think even if Obama did lose NC, it wouldn't as "big" as it would with Biden.
Now that was a mistake on Hillary's part. She should have gone with either like you said Sherrod Brown or Cory Booker to try and not depress the black turnout rate as much as Kaine did in OTL. I know he didn't have much experience, and it's usually not a good idea to have running mate states close to each other, but Obama didn't have much experience either and still won. Plus, Bill Clinton picking Al Gore for running mate was a mater stroke.
In general, it's all about the timing.