Who is in charge of vetting the presidential candidates?
That is the major determination that needs to be defined imo. It isn’t defined in the Constitution or by federal statute to my knowledge. The Constitution leaves somethings vague or without detailed direction. It provides for the process of electing a President and the roles played by the states, the electoral college and congress but doesn’t provide specific direction as to determining how a candidate is vetted to meet the Constitutional requirements that you enumerated.
States could require specific infomation before approving a candidate’s position on the ballot, Congress could demand specific information before approving the Electoral College vote or the Constitution could be amended to provide a method of proof. But as you say who has the responsibilty today.
You hit the nail on the head...the constitution was written in vague terms, with no recourse, so the states will be given the control. (it does discuss consequences if federal crimes are committed by the president)
Fine, but that does nothing about the current president, citizen or not.
The state of CA has had cases where people were tossed out fo the election because they were not eligible.