I updated my OS to Big Sur but have problems running my apps. How can I go back to Mojave?

Revert your Mac to a previous macOS version - Apple Support

Keep in mind always backup your data before installing anything.

Catalina and Big Sur are only compatible with 64 bit applications.

Until you know you have all 64 bit versions, there is no reason to upgrade to these systems. You can keep a separate partition if you want to use specific new programs, but only migrate once your whole library is compatible.