If we made modifications to the individual screens for the kiosk profile (text, button names and settings, etc.), do we need to copy those to the new update code folder or will it automatically do that?

If the modifications were done in "Configure System", these will stay intact even after updates. No manual steps are needed. If any changes were made to a file directly, which we do not recommend, we cannot answer this question without getting information about the file and the change.