This has one very specific exception I was referring to, which is explicitly spelled out in Article V,
The first clause of that sentence is obviously no longer valid, but direct your attention to the second clause: no amendment that will change the equal distribution of Senators may be made without the consent of each and every state so affected (that is, all of them). Therefore, any amendment that would change the composition of the Senate by making different states have different numbers of Senators would either have to explicitly repeal this clause or be unanimously adopted. If either of those were not the case, then the amendment would itself be unconstitutional.
Untrue. Provided that you accept the principle of judicial review at all, then the Supreme Court clearly has the ability to reject amendments that are passed in violation of Article V's statements on how to amend the Constitution, because such amendments themselves violate the Constitution. For example, if an amendment was added after a national popular referendum, without a prior amendment adding that to Article V as a method of ratification, then it would be an ipso facto invalid amendment, because to amend the Constitution you must have approval of 2/3rds of Congress or have 2/3rds of the states request a convention, then have 3/4ths of the states approve the amendment, not a national popular referendum.
There have been no amendments that have actually violated this provision, so it is of course theoretical. But if you accept judicial review at all, then this is a clear power of the courts.
If the Supreme Court struck down the 21st Amendment they would clearly be going mad, because that was passed in perfect accordance with legal procedures. I was referring to amendments that either sought to alter Senate distribution without either the consent of all the states or removing the protection clause first, none of which have been proposed, or to amendments that were passed aside from Article V's procedures, again none of which have passed. There is also the possibility of amendments that violate self-limiting clauses in their formulation (e.g., section 6 of the 20th Amendment, "This article shall be inoperative unless it shall have been ratified as an amendment to the Constitution by the legislatures of three-fourths of the several States within seven years from the date of its submission."), but this is again a theoretical question.
But, provided you accept judicial review, there are clearly situations where the Supreme Court would be justified in striking down an amendment as illegal.