How an app can detect my device's uniqueness?
As RossC said, yes it depends upon the developers how they keep the logic to detect the uniqueness. As I am too a dev (Windows App) and my preferred way is to keep the device id's over the cloud. So whenever the device gets internet on, it syncs with our servers for prior installations and it becomes easy for users to use it on multiple devices. Other easy ways are to put some file inside the android system folders like data , usr or wherever.