I have a department with an ACD group. I also have an App Builder application set up for them. When they log out of their queue, they want the caller to hear a "we're closed" greeting. I have the queue NCFW to their mailbox. How do I set up an Information only mailbox, so that callers can't leave messages, and not hear the "mailbox is full" response?

You have to create Info MB at the time you are adding one. CP will give you a choice what type of MB to create Subscriber, Guest or Info.

You could use the existing mailbox. Record and use the ALT greeting. ALT greetings have an option to disable leaving a message.

I didn't see the options for Subscriber, etc ...and doesn't the system require a response as to when the temporary greeting expires?

No expirey. Subscriber/info option is there on the mailbox setup screen.