Yes, the private key never leaves your machine.

You send them a certificate signing request with your public key, they put their verification stamp on it and send it to you.

The only part they have to play is verifying that your certificate is trusted by a root certificate.

The CA cannot decypt: they don’t have the secret key which only the server has. When requesting a new certificate from the CA, the server generated a secret key (aka private key) and then generated a derived public key that goes into a Certificate Signing Request (CSR). The CSR is what the CA receives, not the secret key, and then the CA returns the certificate file to the server, which has been endorsed by the CA and thus trusted by the user base.

Phrased another way, a certificate is the instrument that confirms that a purported public key can in-fact be safely used, and that no MITM attack is happening (assuming you trust the CA that signed the cert). But once you’ve confirmed the public key, the rest of the cryptography is public key cryptography, meaning the secrecy of the secret key is the whole game.

The certificate is only used for authentication. The actual data is encrypted with a temporary symmetric key that is generated via a diffie-hellman exchange

Even if they had your private key they still wouldn’t be able to decrypt the data

They don’t have your private key