...which means that apps don't have to do anything to get backed up. I haven't tested iCloud Backup myself, but I'm 97% sure that it will backup and restore Music Studio's files if you have enough iCloud storage.
In general, Apple and Google will never charge you twice for the same app. If you're logged in with the account that you used to purchase the app, you can download it as often as you wish, on all your devices.