Re: Open ticket display:
Opening a ticket is the act of opening a ticket... Tickets do not have Departments until after they are created. So there wouldn't be anything to display on the open ticket page...
For Agents the Department is already displayed when you view a ticket.
For Users the Department is already displayed when you view a ticket.
Re: Ticket View:
I don't think that section breaks work that way... but I have asked the Devs to take a look at this thread to see what they have to say. I suspect that you would have to customize the product yourself by editting the core files to display the section breaks.