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Article 2, Section 4 of the US Constitution states:

The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.

This clause apparently lays out the requirements for removing a US Office, and requires that the Officer being impeached commit "treason, bribery, or other high crimes and misdemeanors".

Does that clause mean that that the FULL EXTENT AND LIMIT of impeachable offenses are those listed?

For example suppose a Party managed to gain control of 2/3 of the Senate and the House and they decided to impeach a sitting President of another Party for purely political purposes. I.e. the President did nothing, but the Congress impeached anyway, or the Congress invented some specious charge to justify the impeachment.

In that case could the Supreme Court overturn an Impeachment?

In Walter L. Nixon v. United States (unrelated to President Richard Nixon), the court held that the judiciary could not review impeachment proceedings. According to the constitution, the House has the "sole power of impeachment" and the Senate has the "sole power to try all impeachments." The Supreme Court considered this sufficient evidence that the framers did not want the judiciary involved. Further, because judges themselves can be impeached, it would violate separation of powers to allow them to review such cases.

Other answers have covered whether SCOTUS can overrule and impeachment and/or conviction of the President, so I won't rehash that. As to the other part....

Does that clause mean that that the FULL EXTENT AND LIMIT of impeachable offenses are those listed (Treason, Bribery, or other high Crimes and Misdemeanors)?

Yes, but it doesn't matter.

Treason? Distinctly defined.

Bribery? Also a specific crime.

"other high Crimes and Misdemeanors?" (emphasis added) - pretty indistinct, so it means "and anything Congress thinks would merit removal." The feeling was that it was intentionally left vague so any serious abuses of office or powers that the Founders were unable to remember to list, exhaustively, or anticipate ("they forgot about playing Nickelback over the White House PA system!"), would not get a free pass. The idea was probably that Congress wouldn't abuse their powers in this regard in trivial partisan fashion, so they left it a bit open-ended and up to Congressional discretion.

So, you know, the Founding Fathers might have underestimated the pettiness of future generations, to a certain degree.

Here's some reading on the broad range of how people have tried to interpret the phrase "other high crimes and misdemeanors" -

Slate: What Are High Crimes and Misdemeanors?

To better clarify Nixon v. United States that @eyeballfrog mentioned, SCOTUS found that impeachment is a purely political matter, not a legal matter, and thus SCOTUS cannot rule (Though they can rule on the question of "Can they rule on impeachment" which does ask a legal question, the answer is "No, we cannot rule on an impeachment"). For a less politically contensious restriction, the question of "Are we at war?" is also considered a Political Question and the Courts have no power to rule on the legality of the proper authorities to declare a particular war on another nation.

Thus, Impeachments are all about politics, however of the two impeachments of the President, both were decided in favor of the President. In fact, the impeachment of President Johnson was decided by one vote (by a Democrat Breaking Ranks) who concluded that the charges were drummed up to justify a political removal by Impeachment, not one for behavior unbecoming of the office.

It's suspected, though not known for sure, that an overtly political impeachment of the President is going to go badly for the Party opposed to the President, the voting public would be upset by the move. While Nixon (Yes, the more famous one) was never impeached, his resignation came when he learned that the Impeachment charges had gotten out of House Committee and had enough votes to clear the house and make it to the senate, where the vote tally to impeach over Watergate had been known for much longer.