How are all necessary parameters shared between signer and verifier in the ED25519 signature scheme? I want to use the ED25519 signature scheme in my application which requires frequent sharing of secret data between two entities in the public domain.

I know that the Schnorr signature scheme has a key authentication center (KAC) which decides and shares common parameters to be used by signer and verifier. The KAC also signs the public keys of everyone with its own private key. And then the signer signs the message and sends his public key along with the signature to the verifier [From Schnorr's paper 1991].

But is there any KAC in ED25519? And what are the parameters shared in ED25519 by the KAC?
Ed25519 is well-defined and requires you to use SHA-512 as internal hash function along with the twisted Edwards version of Curve25519, hence there's no need for a KAC when it comes to questions about the parameters. As for the integrity of the public key, there's not yet a standard for Ed25519 based certificates so there would be a custom solution needed for a given application.