where is ‘independence’, ‘freedom’ or ‘liberty’ defined in the Constitution?
'Freedom' is not used in the Constitution. It's in the Fist Amendment, and the meaning can be implied by the sentence before it - 'free exercise thereof'. 'Independence' is also defined by the way it's used: "done in Convention by the Unanimous Consent of the States present the Seventeenth Day of September in the Year of our Lord one thousand seven hundred and Eighty seven and of the Independence of the United States of America the Twelfth." By that you can infer that they define independence as the political separation from Great Britain. "Liberty" is contained only in the Preamble and is not defined; maybe it should have been?
But enough of the nonsense. Where does the Constitution or U.S. law define natural born citizen the way you define it?