Certificates implementation in "SSL forward proxy client and server authentication" scenario.

The client SSL profile is used to manage the SSL session between the client and the proxy. The server SSL profile is used to manage the SSL session between the proxy and the server. For client side SSL, you need at a minimum a server certificate and private key in this profile. This is the certificate that the server (F5) will present to the client during its SSL handshake. You can further configure client side mutual authentication here (client certificates), but it doesn't sound like you need to do that. For server side SSL, the proxy is actually the client in this SSL handshake, so there's usually very little you have to do here. In fact in most cases you can use the built-in serverssl profile with no modifications. The only time you'd add certificates and/or CA chains to this profile is if you're required to do explicit certificate validation and/or mutual authentication in this SSL handshake, which is rare.

To the subject of your question though, forward proxy SSL is something completely different. This is when the F5 is in forward proxy mode and you want to decrypt and re-encrypt outgoing SSL traffic. You're trying to access servers internal to your environment, so this is a reverse proxy.