Does Catalina detect and warn about incompatible apps?
32-bit apps in Mojave should already bring up a warning when you launch them.
You can check what 32-bit apps you have in System Information: Click to open the Apple menu, then hold Option and click on System Information, which appears where 'About This Mac' was.
Then choose 'Applications' from the sidebar, under Software. This will show you whether the app is 64-bit or not. You can sort the list by that column, giving you all the apps in one place.

Catalina will not remove any apps: it will just leave them in place.