"Does he not know?" is current usage. This is a bit counterintuitive, given that "Doesn't he know?" deconstructs to "Does not he know?" which of course isn't "correct". But that's English. :)
As Maulik says: "She doesn't know?" is a declarative question. It is often used to convey a strong expression of surprise. For example, suppose you had heard that your best friend had gotten a new girlfriend. You were getting together with them to meet her for the first time. It turns out that the girlfriend is your cousin's ex-wife; the divorce went through just a week ago. The conversation might go something like this:
You: She's your girlfriend?
Best Friend: Yep.
You: Seems a little early for you to be dating my cousin's ex-wife, since she only got divorced a week ago. How long have you been dating?
BF: She's your cousin's ex-wife?
You: Yes. You didn't know?
BF: No, I didn't know. (to girlfriend) And you only got divorced last week? Why didn't you tell me?
You (interrupting, to GF): You didn't tell him?
GF: It's complicated...
They are expressing surprise to the point of incredulity about the situation.