These questions may all be related - how old is the phone? The S3 was new several years ago, so it may just be getting old. You can try disabling TouchWiz and see if that fixes the error message and the other two issues. -to/google-android/how-disable-touchwiz-on-samsung-smartphone-3601797/
Try finding the Application in Settings > Applications and clearing the application data. TouchWiz Home is your home screen (the thing that stores all of your apps and widgets). Something may be running on it which is crashing the home screen. Usually a widget. Or the phone could be running out of RAM, meaning you'll want to check to see what apps are running in the background and uninstall (Don't use Task killers!!!) the problem apps. Facebook and Messenger are two big hogs in and of themselves.
Resetting TouchWiz Home may clear any customizations you've set. They can be redone easily, however. If problems begin again after customization, you'll want to track down where the crashes started from based on what was added.
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