Where in the constitution does it permit the judiciary to remove an executive? It doesn’t. The constitution doesn’t prohibit a lawsuit but the court has already address these issues in Jones V Bush and Bush V Gore.
Where in the Constitution does it permit a president to be impeached for failing to be eligible for office?
If there is no consequence to the eligibility requirement, then why is it there?
Having either composed briefs or written published articles in both cases, I am curiouis as to what you are referring to. If you are referring to the Paula Jones case in particular Clinton seems to have lost on any issue even approaching what you mention. As to Bush v. Gore, the Constitution was upheld, the prescription of the state legislature mandated by the Constitution was upheld and I don’t see where any issue you seem to be intimating was decided there was even at issue. Can you explain?