As mentioned in your first post, we support caching static resources (images, CSS, Javascript, etc...) through the storage configuration so long as your CDN has it's own internal sync'ing.
Caching the whole website is getting to be outside our scope of support as this is leaning more towards hosting and CDN providers than really the software. As Randy mentioned, there is a degree of complexity here that we can't really assist with on the CDN side but if there are questions on our software side how to do things which your CDN may require, we can answer that. Alternatively, I can move this to the Community Support forum if you require more guidance on the CDN side of things.
You would need to ask your CDN provider if they support dynamic websites that have authenticated sessions. You will need to ensure you are not caching data, whole pages, and sessions which are session specific. It is not as simple as throwing static resources over to a CDN and asking them to cache and display everything.