The main point of the article is what the minimum fonts are you need in a given version of OS X. So no, it does not cover all of the OS X included fonts.
Personally, I am having no issues at all with fonts in El Capitan. However!, there is a known bug. And that is:
You cannot put Type 1 PostScript or older legacy Mac TrueType fonts into the root /Library/Fonts/ folder, or activate them in place with any font manager. If you do, they may, or may not appear in all, or any apps. They must be either placed directly into the Fonts folder of your user account (which is where Font Book will copy fonts to automatically when added in the default manner), or they must be added to your third party font manager's physical cache of activated fonts. For instance in Suitcase, that means adding them to the Vault, not activated in place. OpenType fonts do not have this problem.
No, there is no such software. If you want the system put back to the default fonts only installed by OS X, open Font Book and run the menu command, Restore Standard Fonts. This will move all third party fonts out of the System and root Library Fonts folders to a new folder which will be created next to each Fonts folder. If you have removed any OS X fonts that also exist in the hidden Recovery partition, those will be copied back to their normal locations. Any others will not come back without reinstalling them.
The command does nothing to your user account Fonts folder. So the last thing to do there is to move all fonts out of your user account Fonts folder to the desktop, or some other location where the OS will not see them. That is, not in any of the three working Fonts folders (System, root Library, the logged in user account).
Close all applications. In the Preferences folder of your account, put the file com.apple.FontRegistry in the trash and restart. That file is Font Book's database. Removing it and restarting will clear any possible issues with a corrupt Font Book database, which tends to be easily damaged.
Lastly, clear all font cache files from the system. Close all running applications. From an administrator account, open the Terminal app and enter the following command. You can also copy/paste it from here into the Terminal window:
sudo atsutil databases -remove
Terminal will then ask for your admin password. As you type, it will not show anything, so be sure to enter it correctly.
This command removes all font cache files. Both for the system and the current logged in user account. After running the command, close Terminal and immediately restart your Mac.
Barring any issues with the OS itself, or damaged fonts, this will clear up all font issues and thing should work as they're supposed to.