Does all the certificates of a certification chain share the same public key?

I recently got a certificate, private key included, signed by DigiCert that embed all the certificates of its certification chain, client, intermediate and CA. When I look at the public key of all the certificates of the chain, it's the same.

Is this normal? Or a special case?

Since I know the private key associated to the public key of my certificate, and the CA certificate has the same public key, do I know the private key of the CA?

Do I miss something?