Thanks for your tips.
I uninstalled Avast Free, then did a reinstall. Currently (using Windows Explorer), the Profile Folders contains two AVAST folders, one with no files or folders, the other with 355 files and 20 folders.
Another oddity is the second AVAST folder (with 355 files) does not show the expansion arrow in Windows Explorer, not does it allow me to see the files or folders. I wouldn't expect the first one to have the arrow since there are now files or folders, but the second one should show it.
So, the questions of the day are
* Why do I have two AVAST folders (even though one is empty)?
* Why doesn't the populated one have the expansion arrow?
* Even though I have two AvastUI.exe icons in the 'Notification Area Icons' box, with both set to 'Show icon and notifications,' and Avast is running, none of the icons appear in my System Tray.
Any thoughts, suggestions, on the above?