By design nothing in the chain can be altered. But of course you could have a block indicating "person X is now person Y". But you can always read that Y was at some point X (and at what point the change happened). That would not be good, as it would be a public ledger of all trans people. It would also make things like witness protection impossible because inserting a block "today in 2024, person W was born in 1974" is very suspicious

Same with corrections.

These are actually very good questions. As far as when it's immutable, that's almost immediately because of the hash power of the network. After about 60 minutes, you can really trust that it cannot be reversed. As some other comments mentioned, you would update the database throughout time rather than modifying the original entry. So you could still trace it back. I saw some comments about witness protection programs and trans protection. And I think that would come down to data management with things like fully homomorphic encryption, allowing for checking whether something is valid, even an encrypted format without having to decrypt it and know the contents. So someone could tell you they exist and then they could point you to their entry on the blockchain and you can see that indeed they exist without knowing anything about them.

A simple test would be something like, I want to order a drink, so I go into a bar. I sit down and the bar person asks me for ID. I give them my entry on the blockchain, and then they check to make sure that the entry was created at least 21 years ago. Since I did not hand over my ID, they don't know my name unless I give it to them. They don't know my street address and other details that would be on a currently government issued ID.