Hello,
Sorry to hear you are having issues. Have you tried by going to application list->Browse for an application in the application list->Right click on it->Pin to Start11. Something like screenshot below.

Also, how do I restart Start11 when it goes bonkers?
You can try restart Explorer.exe. There is a Restart Explorer button on Start11 (Windows 11)->taskbar area. Or you can use this guide to do restart explorer.exe https://www.howtogeek.com/198815/use-this-secret-trick-to-close-and-restart-explorerexe-in-windows/
Thank you,
Basj,
Stardock Community Assistant.