I have read a lot about this stuff, which has been around since 2008 at the latest. But I really haven’t completely mastered it.
What about the age of Obama’s mother? Often that’s discussed in these arguments.
His mother's age is only material if he was born outside the country. If he was born in the states, he's a citizen irrespective of his mother's age, and I suspect that if the court were to define NBC, they'd hold that his US birth also makes him an NBC - but, that's just a guess. However, his mother's age wouldn't be relevant.
If Obama was born outside the US, his mother's age is germane. In fact, it's possible because of her at the time of birth, he may in fact not be a citizen (to say nothing of NBC) because of the US law at the time of his birth. Sounds crazy, but it's true. Of course, him being born someplace other than HI is a big "if".