No, you don't want your whole site to be https.........just the areas that need to be (zen-cart will handle that.......once it's configured to use SSL).
Maybe you DO already have SSL and just don't have ZC configured to use it?
Log into your cPanel, click on "SSL/TLS Manager", then on "certificates (CRT)". It will tell you if there are no certificates installed on the server, or show you the details of your certificate (if there IS one installed). Then you'll know FOR SURE if you have SSL, or not.
Hope this helps.




