It's not uncommon to see contracts which prohibit amendments, or require them in writing. But you can amend them, often even orally, to delete that provision and substitute a new one. That is a long-standing principle of law.
I'm not suggesting that such a prohibited amendment would survive court scrutiny, or much less that we can orally amend the Constitution, but I would suggest that it's less clear than it might appear.
Yes, provided such amendments are agreed to by all contract participants. Suppose, however, that a contract contains provisions whereby a certain subset of the original signers can make amendments to it, but with certain exceptions. Would not the removal of those exceptions require unanimous consent, as distinct from the subset consent required of other changes?