Why does this sentence not end with है ?
You can drop the 'hai' if the sentence is negated. I don't recommend doing it though.
Let poor Peter sleep :'(
I think that Duo wants us to know that Peter has the ability to not sleep, not that he is forbidden to. He CAN not sleep: वह नहीं सो सकता है। He can't sleep: वह सो नहीं सकता है। but that's a wild guess...