Can a app store data beyond uninstallation?
A lot of apps leave behind what I like to call junk files.

There's an app called SD Maid which helps you clean up your F.S. (filesystem). There is also Ccleaner and System app remover, these apps will assist you in cleaning up cache and removing apps. You can also navigate to /sdcard/Android/data/ and remove any left over folders an app may have left behind.

What I like to do is clear the apps cache and then uninstall the app. I hope this helps.