Yes, you are a US citizen if you are born to citizens, regardless of the country you are born in. However, if you are born in a foreign country you are NOT eligible to run for President.
US Military installations might be a different matter. But it is a fact that if your parents are on vacation in the Bahamas and you are born there, you can not run for President.
That is incorrect. The exact opposite is true, you are eligible to run for President.
What are you basing your opinion on? The Constitution says you have to be a natural born citizen. Are you saying that a natural born citizen is only one that is born in the US?
US military installations ARE a different matter. They count the same as the U.S., for these purposes.
It isn't as if this wasn't all figured out before McCain ran the first time.