Constitutional amendments are not interlineated with the text of the original Constitution, but instead stand alone as statements of their action. Each amendment does not go back and revise individual words of the Constitution, but instead essentially functions as a document that says “Notwithstanding anything to the contrary in the Constitution or any prior amendments...” and then states the substance of the amendment. A notable exception is Amendment XXI, which repealed Amendment XVIII (the Prohibition Amendment). So I think this addresses most of your questions. The amendment process is actually somewhat complicated, given it relies on the interplay between Congress, the states, the executive branch, and independent agencies. It’s also notable as one of the few important processes of the national government in which the president has basically no formal role whatsoever.

According to the National Archives, the Archivist of the United States is the officer tasked with handling the ratification of an amendment, and the Archivist follows substantially the same procedures as were followed by the Secretary of State prior to 1950, when the duties relating to ratification were transferred to other officers of the federal government.

An amendment can be passed by a convention of the states, or by the passage of a joint resolution (notably, a joint resolution does not require the signature of the president to take effect). To date, all 27 amendments have been proposed by a joint resolution of Congress.

Congress passes a joint resolution proposing an amendment to the Constitution, the original of which is sent to the Office of the Federal Register (“OFR”), the official publication that lists proposed administrative rules and agency actions for public notice and comment. The OFR prepares an information packet to accompany the joint resolution, and then the joint resolution and packet are sent to each of the 50 governors of the states. As each state ratifies the amendment according to its own legislative procedures, an original of such ratification legislation is sent back to the OFR, which checks for facial legality and then acknowledges receipt of the same. Once the OFR has received ratification legislation from three-fourths of the states, a formal proclamation is published by the Archivist in the Federal Register and US Statutes at Large, following which the amendment is valid. The amendment takes effect immediately unless the amendment itself otherwise provides (for example, Amendment XVIII [Prohibition] took effect one year after the date of ratification).

Source: https://www.archives.gov/federal-register/constitution

Edited to correct a few typos.