public key infrastructure – Diffie–Hellman key exchange in TLS 1.3

I am reading about the Diffie–Hellman key exchange in TLS 1.3. So the first step here is that the two parts Alice and Bob t agree on a large prime p and a nonzero integer g modulo p. Then Alice and Bob make the values of p and g public knowledge.

How the values p and g get public as we are before the client and server hello messages?

Also, the private and public keys that get generated here are the same keys that the server or/and the client use in order to acquire a cc.509 certificate (via a certificate signing request to a trusted certificate authority)?