Hello Kathryn,
Thanks for reaching out to the Apple Support Communities! From your message I understand that currently the #images and Memoji Stickers apps are not working in Messages on your son's iPhone 7.
You've done some great troubleshooting to try to resolve the issue up to this point. You mentioned that you're unable to make any changes to the Favorites or toggle on any of the other apps in Messages. Check to see if there are any restrictions turned on his iPhone: Use parental controls on your child's iPhone, iPad, and iPod touch. If there are any, be sure to turn them all off, and then follow the steps to toggle the apps back on: Use iMessage apps on your iPhone, iPad, and iPod touch.
If there were no restrictions, the next step I'd recommend is reinstalling the iOS. Messages is an app built into the iOS, the only way to reinstall it is to reinstall the iOS. If the iOS can be reinstalled, the data on the iPhone will not be changed. It's always a good idea to first make a backup of the iPhone data. Having a backup of your data is like having an insurance policy, you don’t plan on using it, but it’s great to have if you need it. Here's how to back up the iPhone: How to back up your iPhone, iPad, and iPod touch.
Next, follow this article to reinstall iOS 13.1.1: If you can't update or restore your iPhone, iPad, or iPod touch. When you get to step 4, be sure to select Update. This will allow the computer to try to reinstall the iOS without any changes to the data. Once the update is complete, see if there's any change with his Memoji Stickers and the #images app.
All the best.
