Does Ethereum have some sort of system built-in to be able to internally and correct as the community learns about new issues? AFAIK everything that's written is written in stone, no? (Barring a majority decision agree to a new ledger entirely like they did that one time)
That would just be the normal upgrade process. You'd submit an EIP, it would undergo review, a spec would be developed, and it'll be worked into the client development and release schedule.
Yes: much like other standardized software. Many people coordinate and agree on patches and new specs, and then developers work toward implementing and testing it across clients. This is how all forks have happened so far, including “patches” like EIP-1559, and how it will continue.
Yes, Vitalik asks everyone to download a new version with the protocol patched. Previously it was "pretty please do this", now it is "do this, or you lose all your staked ETH".