Schedule Auto Shutdown on Android
Natively, there is no way to schedule shutdowns and boot ups of the Android system. If you do decide to root there are applications in the Play store that can shedule a shutdown (you may even be able to make your own busybox script instead). However booting up will never be possible the way Android handles shut downs because when Android shuts down, it is not running.And so, there is nothing in memory to initiate any sort of startup process.