I have no idea if the corruption is in your profile or an update "went bad." I'd do what RC suggested and export your bookmarks, download a fresh full copy of Firefox from mozilla.com, uninstall Firefox and then install the fresh downloaded copy of Firefox. I'd also suggest making a copy of your Firefox profile as well. Here's how you do that:
https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data
The problem with just installing a freshly downloaded copy of Firefox this way is that your existing user profile will remain untouched so if the problems go away then good but if the problems remain then there probably is something messed up in your user profile.
To address a corrupted profile you will have to use the Firefox Profile Manager. Directions on how to use Profile Manager are here:
https://support.mozilla.org/en-US/kb/profile-manager-create-and-remove-firefox-profiles
You can create a new profile and then import your bookmarks to the new profile. When you create a new profile uncheck "Don't ask at startup" so that you can jump back and forth from your new to your old profile until you are comfortable with the new profile. With that checkbox unchecked the profile manager will show up every time when you start Firefox. When you are satisfied with your new profile then select the new profile and check the box and you won't see it again until you intentionally start up Profile Manager again.
One Firefox feature that you may also want to consider using is Sync. It is a bit trickier to set up and use but once you get the hang of it, it will be quite useful. Sync can store your bookmarks, your passwords, your Firefox preferences as well as other data. You can select which data you want Sync to save. Your Sync data is encrypted btw (see the "Firefox Sync data is secure" link in the link below). When Sync is used you can access Sync when creating a new profile and your bookmarks, passwords, etc. (whatever you allowed Sync to store) will automatically be downloaded and your profile updated.
https://support.mozilla.org/en-US/kb/firefox-sync-take-your-bookmarks-and-tabs-with-you