Yep. This isn't even a close call. It's well settled law that states control their own ballot access, not the feds. The states couldn't impose additional requirements for presidential eligibility, but they're certainly entitled to verify Constitutionally mandated eligibility criteria.
Yes, Correct.
The OP seems to want to suggest that this is just an unfounded witch hunt. That could not be farther from the truth. There is a reason this issue won’t go away and it’s real simple. The pile of evidence that Obama was born in Kenya to parents that at least one was clearly not a US citizen is overwhelming!
In the end it is extremely unlikely that Obama is eligible to hold the office of the presidency. The only thing undecided is what to do about Obama and how we resolve this issue with future candidates.