Then the child has mixed loyalties to its parents citizenship. The object of Natural Born Citizen requirement for office of President is to remove mixed loyalties so there is no question. Like Trump. Not like Obama or Harris.
Your second point is outside the scope of US President qualifications of Natural Born Citizen.
Your third point left out the consideration of "and subject to the jurisdiction thereof" yet again. So it, too, is outside the scope of US President qualification of Natural Born Citizen, so don't expect another reply.
RE: the object of Natural Born Citizen requirement for office of President is to remove mixed loyalties
That is NO GUARANTEE if personal loyalty to America. You can, like the American Taliban John Linda Walker, be a natural born citizen yet fight against your country. You can love this country and be loyal to it even if your parents were from another country. There is no guarantee either way.
And since Obama WAS PRESIDENT regardless of whether we like it or not ( I didn’t ), our discussion is simply academic.