Now it’s your turn to answer questions.
Is eligibility determined by plebiscite?
Is eligibility determined by Congress?
Is eligibility determined by statute?
Is eligibility determined by regulation?
Is eligibility a political question?
Is eligibility a policy decision?
Does occupancy of office confer eligibility?
Is eligibility a question of law & fact?
Are questions of law exclusively committed to the Judicial branch?
Are the facts concerning an individual’s eligibility judicially discoverable?
1. Is eligibility determined by plebiscite?
If by that you mean a general election for the Presidency, then there is de facto determination by the electorate. Once the electorate has given approval to a candidate, it's near impossible to imagine the Congress or the Courts seeking to overturn that.
2. Is eligibility determined by Congress?
As among the electorate, the judiciary or the Congress, the better argument rests ultimate determination with the Congress.
3. Is eligibility determined by statute?
This question may be relevant in the case of a person born outside the U.S. Congress certainly would likely accept its own determinations as to those who are citizens at birth. And even a court, in construing the meaning of "natural born citizen" might take into account Congressional intent. Statutes don't make determinations, so the question is poorly phrased. Though statutes might be considered by the determiner.
. 4. Is eligibility determined by regulation?
No.
5. Is eligibility a political question?
There has been a signal from several lower courts that it is. I don't know offhand what SCOTUS cases there have been since Baker v. Carr on topic, so I don't know how that court might lean.
6. Is eligibility a policy decision?
I'm not sure what you're asking here. The eligibility requirements certainly reflect a policy decision on the part of the Framers. As to anyone making a determination today, it strikes me as case of a person either being eligible or not; I don't see where policy factors into answering that.
7. Does occupancy of office confer eligibility?
It's better to say that occupancy is evidence that eligibility requirements have been met and accepted.
8. Is eligibility a question of law & fact?
Yes.
9. Are questions of law exclusively committed to the Judicial branch?
There is a significant exception making "exclusively" incorrect: the Constitution commits to the Congress the authority to determine "High Crimes & Misdemeanors" committed by the President. That involves matters of law and fact.
Since the Congress has the authority to determine if a person is to be removed from office, a strong argument can be made that it is also the proper body to determine whether a person meets the qualifications of the office. Relevant on this point is the further authority vested in the Congress to hear objections to the acceptance of the Electoral College vote, which could entail objections based on eligibility of the person receiving the votes.
10. Are the facts concerning an individual’s eligibility judicially discoverable?
For the matter to be discoverable, the case would have to proceed past the pleading and motions stage. That requires at a minimum a proper plaintiff (standing) and a court with jurisdiction (political question). Those issues will sink most every case at the outset. Even assuming a case passes muster on those points, were the candidate in question to submit the usual state-issued birth certificate form, that would answer both the "natural born citizen" and "minimum age" requirements, likely precluding discovery on those issues. Though there could be an issue on the "residency" requirement requiring further factual exploration.