Well! Thanks to all of you, everything is apparently as it should be. Windows for Firefox, Thunderbird, and others no longer cover the panel at the top of the screen. All Exit, minimize, and maximize buttons are back. I can now drag or resize windows as before. Window pull-down menus now stay put so that I can select from them, I can switch workspaces, and all icons are back; some are different but there. I just don't know exactly how it all happened.
I'll try to tell you what I did as best as I can remember and decipher from my notes:
Because I could not answer TheGhost's question about what I did when Emerald was installed, I reinstalled Compiz and Compiz Fusion and turned it on in PCC to see what would happen. I selected an Emerald theme and this resulted in all the windows corrections mentioned above. No changes to icons, however. Ok. These corrections are nice but Compiz wasn't running and everything was OK before the last system update. So.
I decided to go back to Synaptic and re-install the following:
GDM, Gnome Display Mgr
Gnome-Applets, For Gnome Panel
Gnome-Icon-Theme, Gnome Default Icons
This had no effect even after logging out and back in.
Neal ManBear suggested that I install Shutter. I had Shutter already installed and I'm not sure how it relates to the problem. However, I was considering re-installing it but instead I decided, per Fornhamfred's suggestion, to install Update-notifier instead. As soon as the install completed it told me that there were two updates available; IOManager and Shutter. As soon as it completed the updates of those two apps. most of the missing icons popped up. When I logged out and back in, they were all smiling back at me. With my fingers crossed, I opened PCC and turned off 3D DeskTop Effects (Compiz Fusion is still installed). All is still OK.
Now. Neal ManBear. Was that a coincidence or did you know something?
Again, I don't see how Shutter had anything to do with it. So, it must have been IOManager. Was it the problem all along? Or, did I (we) unwittingly do a combination of things that fixed it?