How do I make the back/next links open only within that div, or at least on that half of the screen?
I'm not sure what you mean by the 'back/next' links on the right-hand side ... I can't see any links like that on the demo page, so if you're talking about something you've done on your own page then you'll need to give us a link.
Words of warning – before you get too carried away with Ajax for navigation, bear this in mind. It completely destroys the way hypertext navigation is supposed to work. Go to that demo page, click on an Ajax link, and then click the 'back' button. Do you go back to where you were before? No, because the browser doesn't recognise it as a change. Bookmark the page, or give a link to it, and you can only go to the original state of the page. Search engines can only find the home state, and may not even crawl the extra content. Right-click and open in new tab, and you just get an error message.
The method they have used is absolutely awful for site navigation, and I would very strongly advise against using it.
Any posts I write in Arial are on my mobile phone, so please excuse typos etc. Any posts I write in Verdana are on a PC, so feel free to berate me mercilessly for any mistakes