1. It is NOT necessary that the President, other officers in the executive branch, or federal judges commit a crime before they may be impeached & removed from office.
Federal judges may also be impeached & removed for usurpations of power (Federalist No. 81, 8th para).
Throughout The Federalist Papers, it is stated that impeachment is for "political offenses".
2. The House has the SOLE power of impeachment (Art. I, Sec. 2, last clause). The Senate has the SOLE power to try all impeachments (Art. I, Sec. 3, next to last clause). The decision to convict is not reviewable by any other body – and common sense tells us what that means! The House may impeach, and the Senate may convict, for any reason whatsoever; and their decision cannot be overturned.
3. The meaning of "Treason, Bribery, or other high Crimes and Misdemeanors" at Art. II, Sec. 4, is far broader than one might at first glance think. Somewhere I saw a scholarly paper showing that the "high" refers to the status of the official – it does not refer to the severity of the offense.
Now, note well! Misdemeanor" has a broader meaning than "a lesser category of criminal offense". Webster's 1828 Dictionary shows the primary meaning is: "Ill behavior; evil conduct; fault; mismanagement."
This shows that a President, Vice-president, and all civil Officers and Judges of the United States may be impeached, tried, convicted, and removed from office for "mismanagement".
4. Errant members of Congress are never impeached – they are expelled (Art. I, Sec. 5, cl. 2).
5. Military personnel are never impeached – they are court-martialed (see UCMJ – Uniform Code of Military Justice), and may be kicked out of the military.
6. It is not feasible to criminally prosecute, under federal law, a sitting President: his prosecutors, the Attorney General and the U.S. Attorneys, all serve at the President's pleasure. He can fire anyone who dares to criminally prosecute him. That is why sitting Presidents who have committed federal crimes must first be removed from office via impeachment, then be criminally prosecuted. (Federalist No. 69, 4th para).
But do not forget: A President may – and should – be impeached & removed for usurpations of power, mismanagement, incompetence, or for any other reason deemed sufficient by Congress.
The lawful methods of getting rid of a sitting President [whether eligible or not to hold the office], in addition to impeachment, are set forth in the 25th Amendment: Natural death, resignation, or inability to do the job.
The 22nd Amendment permits Congress to make laws providing for succession where a President elect has not qualified.
Do not spin your wheels in fruitless insistence that a person (who may still be an Indonesian national) who occupies the office of President can't be impeached because he is ineligible to hold that office. The FACT is that he holds the office. Impeachment is a lawful & constitutional method to rid ourselves of this blight.
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