Flash Player DOESN'T display HTML or graphics outside of Flash containers.
Text, styles, and images are purely HTML and partly your graphics card & NIC (Network Interface Card).
If you're seeing HTML pages (No FLash content) displaying improperly, it's in one of the aforementioned areas.
Thank you, Mike -that clarifies some things about Flash/HTML for me (it's not an area I know much about at all).
From what you say, it seems my problem might be partially Flash (since there is no display inside a Flash container on the Adobe Flash help page, but another page says Flash is up to date on my computer, and so I would expect to see something) and partially something else.
Whether it's partially a Flash thing or not, does anyone have any suggestions where I COULD go for help or what I could look for to try and sort out the issues I mention in my original post?
This page: http://helpx.adobe.com/flash-player/kb/find-version-flash-player.html will tell you if Flash Player is installed, working and what version it is.
If everything looks OK there, it's in your browser.
Note: IE11 doesn't work on that page, as it doesn't on hundreds since it was released in October. THAT, is nothing to do with Adobe or Flash Player, beyond the fact that if a page can't recognize IE11, it won't recognize any plugins in it either.