The default Do Not Disturb settings on the iPhone might be the reason for getting calls despite enabling DND option. By default, iOS only silences incoming calls and messages when the iPhone is locked. That means if you are actively using the iPhone with DND enabled, you will get calls and messages from the users.
When you call a dead phone does it ring?
Answer: A: With a dead battery it should not ring but it should go to voicemail directly.