1. Yes, W3TC is disabled.
2. Correct, no other caching or minify plugins
3. Not sure. Don’t see anywhere on my control panel to clear cache on the host. (UPDATE: found cache management tool and turned off caching, for now.)
4. Correct, not seeing updates. Yes, using the “Visit Site” option (though I’ve tried loading the pages manually and in a different browser. Same result.)
5. On Thursday, I saw my friend’s computer register updates. (But come to think of it, he was on a computer in his office that he doesn’t usually use, so it may have been the first time he loaded the page, at all. What you’re reporting, however is a couple of posts behind the latest, so I’m skeptical that the front page is updating anywhere.
Now, I’ve deactivated widget (Event Organiser and Enhanced Text) and the page still displays without updates. It still has the content from those deleted plugins.)
Just for the sake of having as many clues as possible here:
some pages ARE updating. I can see the sidebar updates and the correct latest post link on a single post page or an event page, for instance.