Per Article 2, Section 1 of the U.S. Constitution, one must be a natural born American citizen to serve as President. Barack Obama is NOT eligible for the Presidency because he is not a natural born citizen. The law that applied during the time of Obama’s birth (in effect from December 24, 1952 to November 13, 1986) stated- “If only one parent was a U.S. citizen at the time of your birth, that parent must have resided in the United States for at least ten years, at least five of which had to be after the age of 16.” We know that Obama’s father was a Kenyan citizen (a British Colony) and his mother just 18 at Obama’s birth...” (thus, she would had to have been aged 21 in order for Obama to be eligible). John A. Bingham, primary framer, 14th Amendment, states- “Every human being born within the jurisdiction of the United States of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution itself, a natural born citizen.” Obama himself has stated that he is the son of a Kenyan- Kenya being a foreign sovereignty. Thus, Obama is not a natural born citizen even if he were actually born in Hawaii.
Aside from that, I believe Obama was born in Kenya.
You are misreading the 1986 naturalization law.
The length of residency and age apply only for births abroad, not births in the US.
As for the meaning of “natural born”, your source is not the law, and there are a host of other definitions. The point here is that the meaning of “natural born” for this purpose has never been defined in law. There are lots of theories and arguments towards backing different definitions.