> What is most useful for me is very general conceptual directions on how to
force certain pages to refresh within a CMS, and a sanity check as to
whether it is possible to force a refresh for only certain content areas on
a page with several content areas.

> My feeling is that it would be possible to force a refresh of certain
pages, but that needs to be done from the html header.  My feeling is that
it's not possible to force a refresh for specific content areas only, but
if anyone knows conceptually how to do this, then I would love to be
pleasantly surprised.

If you're talking about HTTP-level caching, yes. It's controlled by headers on the HTTP response, and thus is page-by-page, meaning both a whole page (URL) at a time, and that for pages to be cached differently they need different HTTP headers delivered with them, by the CMS or web app or web server. 

Some CMS's have their own internal caching, that is not HTTP-level caching and is invisible to the client or user-agent, it's done just inside the 'black box' of the CMS. So even in cases where the browser will not cache the page, where the browser will make a request to the server for the page -- the server may then serve the page from it's own internal cache, for instance to save the time of going to the database and rendering the HTML, just serve already rendered HTML out of an inside-the-server cache.   This kind of cache can possibly operate on a portion of the page, it depends on how the hypothetical CMS is written. 

So that's a conceptual overview. 

With WordPress specifically? People have suggested some WordPress plugins that do caching in various different ways. But when you don't have any control over the WordPress installation? I guess it depends on if they have any such plugins installed, which only they know. 

What is your motivation here?  Just curiosity?  Or are you _wanting_ your pages to be cached, when they are not already? -- if so, why?   Or are things being cached that you do not want cached, and you need to fix it? Or what?