To be clear, she won't be in any legal or administrative jeopardy with the Army just for filing the application for TRO. The TRO has already, and not surprisingly, been rejected, FWIW. She only hits the jackpot if she doesn't physically report for duty at the time proscribed in her orders. She hasn't made any friends at HQAM with this stunt, but she's not going to feel any real heat so long as she complies with the orders of her superior officers, and doesn't make any disrespectful comments about her chain of command, including the POTUS - that is after she reports for duty. Up until then, she enjoys the same 1st Amendment protections as you or I.
As for the rest of your questions, I just don't know. It's not an area of law in which I'm entirely familiar - the complexities and intricacies of HI birth records.
I tend to be a "semantic originalist". IOW, I tend to give much weight to what the framer's intent was when drafting the Constitution. In my reading of the contemporary explanations of the "natural born" clause, I think there's some problem with Obama eligibility, even if he was born in HI. However, I understand the argument from the other side as well, and if forced too, I could probably argue the case that he IS eligible, and be equally persuasive. But, I'm not on the Supreme Court, so my opinion is about as worthless as it can be in this matter. Until this is litigated, it's all speculation and opinion.