Thank you for your post! Mining is not essential for coin creation. New coin introduction can be tied to new block creation, or be time based. Even if you don't use proof of work, you will still have blocks (even if you don't call them that way anymore; they may be called "database updates"). More interesting however, if you don't use proof of work, you don't even need your own currency (but you still could).

Validation is done by full nodes (the "auditors"). Miners also validate, but it is not their primary function. They do so because otherwise their blocks - which indirectly provides their income - could unknowingly be invalid, and not be accepted by the rest of the ecosystem.

Mining has one and only one purpose: providing a decentralized, permissionless mechanism for determining which version of history to accept, in case there are multiple valid competing versions. These competing versions are inevitable when there is not a single party coordinating their creation. This is because communication speed across the planet is not infinite, so one may create a block without having heard about a competing block elsewhere.