Q:

Does the server SSL certificate need to be kept private? 

I understand that private key definitely does, but what about the certificate file?  I also understand that the server sends (part of?)  the certificate to a connecting client, but does it send the entire pem file or does it use some trick to prove to the client it's the correct server without actually divulging the entire cert? 

A:

https://en.wikipedia.org/wiki/Transport_Layer_Security indicates that the server's certificate is given to the client.  The private key is what you want to worry about.