When an amendment is ratified by 3/4 of Congress or by 3/4 of state legislatures it becomes part of the Federal Constitution and all states Even those that did not ratify the amendment must follow the laws in the new amendment to

The statement is true

This is true.

According to the National Archives "The Constitution provides that an amendment may be proposed either by the Congress with a two-thirds majority vote in both the House of Representatives and the Senate or by a constitutional convention called for by two-thirds of the State legislatures."

So, this provides for a Federal and a State option for passing amendments. If it passes by either means, it is binding for the entirety of the county and not just those that passed it.