"Impeachment is a POLITICAL process"
"Impeachment is a political act of the Legislative Branch."
"A person who is not President can not be impeached."
"Article II does not distinguish between ineligibility prior to an election or after, a person failing to meet the requirements is at all times legally disqualified."
"Nothing can be added to the text, it must be taken as it is."
"No person except a natural born citizen, or a citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the office of President; neither shall any person be eligible to that office who shall not have attained to the age of thirty-five years, and been fourteen Years a resident within the United States. U.S. Const. art. II, § 1, cl 5."
Good job.
The other parts need more work. Flesh them out. ;-)
So if a 30 year old person is elected and sworn in, a person who is not eligible, and removal can be effected only by impeachment, what is the purpose of Article II?
Eligibility is a legal matter. Legal matters are handled judicially.