Can't change iCloud settings.

See these How to test an issue in another user account on your Mac - Apple Support

Check that apps are working in second test user account if they are not plan to reinstall the os see this article How to reinstall macOS from macOS Recovery - Apple Support

In addition to trying another user, try the Safe Mode.

Safe Mode - About

Safe Mode Startup – El Capitan. also Sierra

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor. Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown.

Etrecheck – System Information

Might be a corrupt .plist.

Do a backup, preferably 2 backups on 2 separate drives.

Quit System Preferences.

Go to Finder and select your user/home folder. With that Finder window as the front window, either select Finder/View/Show View options or go command - J. When the View options opens, check ’Show Library Folder’. That should make your user library folder visible in your user/home folder. Select Library. Then go to Preferences/com.apple.systempreferences.plist. Move the .plist to your desktop.

Restart the computer, open the application, and test. If it works okay, delete the plist from the desktop.

If the application is the same, return the .plist to where you got it from, overwriting the newer one.

Thanks to leonie for some information contained in this.