“I have another question: If it’s discovered that Zero is constitutionally ineligible, are all of this Executive efforts thereby invalidated?”
No.
The Constitution in Article Two, Section Four states that the only legal process, criminal or civil that can be taken against a sitting President is impeachment to remove that President from office.
The House of Representatives has the sole power to impeach and the Senate has the sole power to try a sitting President for high crimes and misdemeanors. Being ineligible would have to be determined to be a high crime or misdemeanor in a Bill of Impeachment that would be tried in the Senate.
If it's discovered that Zero is constitutionally ineligible, are all of this Executive efforts thereby invalidated? Probably, certainly there will be no end of defendants arguing that.
But since nothing like that or this has every happened before:
No Body FReeking Knows