Suppose I have an iOS 7 device (e.g. iPhone 5), and it is regularly backed up to iCloud. Would it be possible to restore this backup on an iOS 6 device (e.g. iPhone 3GS)?
It's not going to work. You can backup your contacts and things of that nature, but messages, app data, settings will all be lost if you choose to downgrade to iOS 6 from iOS 7.