"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.