I tried REFRESHING Firefox and after about 10 minutes it finished. The Frequent Sites on the NEW TAB are still gone. They were there briefly again but disappeared. All the bookmarks are still there when I go into SHOW ALL BOOKMARKS. Also now the folder icon OTHER BOOKMARKS is gone.

Sorry to hear your Refresh did not work correctly. As the first step, could you do a result shutdown and restart of Windows 7 to release any locked files that may be preventing Firefox from showing your bookmarks.

Then after that, you might consider bringing back your old profile from before the refresh. I'm providing a step-by-step link for that. Note that even though it refers to Windows 10's File Explorer, the Windows 7 explorer is nearly identical.

https://support.mozilla.org/en-US/questions/1322197#answer-1384732

Once you have your old profile up and running we can resolve why the Top Sites section of the new tab page isn't appearing. You could check the settings section here:

Customize your New Tab page to hide or display content

I was able to work around the problem without applying the changes you suggested. I downloaded an aquarium app from Facebook that gave me back the "Other Bookmarks" folder plus a menu bar for holding bookmark favorites. I still don't have the "gear" icon but so far I'm not missing it.

An app from Facebook? Are you sure it's trustworthy?

I downloaded Malware Fox AntiMalware and it ran a full system check. It did flag the Aquarium Lite addin from Facebook but I think that was because it was adware. Anyway I accidentily had it clean the app BUT on the plus side I still have the bookmarks toolbar and the "Other Bookmarks" icon. Essentially I have restored the functionality I lost.

I do miss the aquarium but it had a very large "search box" that I found VERY annoying.