The attestor gives you a credential once. You can think of it as a dob (in e.g. days since 1900) with a digital signature.

Then when you want to access something age gated, you locally generate a proof that says “I have a credential signed by X, with DoB N, and N < CutOff date” where X and the CutOff date are public but the credential and the value N are hidden through the ZkP.

The attestor isn’t involved so doesn’t learn anything. The Verifier only learns the public information, and generally won’t be able to tell if two proofs are made with the same credential.

AFAIK, If the scheme is designed properly, then no. The attestor only knows who they have issued certificates to and the verifier only knows that they have a user that has been verified by that user. Neither the attestor or the verifier can link the two any further than that, even if they collaborate.

That depends on the setup but is not related to the ZKP part. “who is requesting the proof that person X has a gov ID where age >= N” is irrelevant in the context of the proof.