No. Both he and John McCain are ineligible, while Obama is eligible.
Since both of McCain's parents were citizens, you'd have to use a definition of natural born citizen different from that of the Naturalization Act of 1790 to find that he was ineligible.
Yes. Naturalization Act cannot define the term "natural born citizen". Only the Supreme Court can. Or a constitutional amendment.
My definition is anybody born on the territory of the USA.
The idea that anyone called upon to decide what the term means won't consider the definition given by the same group of people who made that a qualification is ludicrous. They likely wouldn't use the exact 1790 definition since it has some gender based distinctions that aren't in keeping with current laws for determining citizenship. But in any case, it's clear that the term is not limited to jus soli. The clear intent of the term as demonstrated by the 1790 act is that it includes anyone who is a citizen of the U.S. from the moment of their birth.
The Supreme Court would, of course, consider the original intent of the lawmakers who included the "natural born citizen" clause in the Constitution.
I wonder, if that is so clear-cut, why they didn't amend the Constitution and why that definition of "natural born citizen" was withdrawn from the subsequent Naturalization Act of 1795?