In Default.aspx DotNetNuke set the Authenticated Cacheability for authenticated user, the default is ServerAndNoCache. For unauthenticated user the ASP.Net default is Privat. So if you login, there is a difference.
The NoCache in HttpCacheability.ServerAndNoCache and HttpCacheability.NoCache disables caching to force the browser to requery the server for the most up to date data or to prevent posting data twice. The back button or history.back() pulls a page from the browser cache, if the page is expired you get the warning.
The behaviour of your Site also depends from the Browser you are using, because they work differently.
You have a DotNetNuke module with a Gridview and paging enabled.Go to page 1,2,..,n
a) You are not logged in, the HttpCacheability is Privat (ASP.Net default)
click the browser back button and everything works OK (IE7 and Firefox)
b) you are logged in, HttpCacheability is ServerAndNoCache (DotNetNuke default)
IE7: click the browser back button and you get an expired message.
FireFox 18.104.22.168: click the browser back button and you don't get an expired message, it works OK
try to set Response.Cache.SetCacheability(HttpCacheability.Privat) on Load of your Control but this can affect other modules on your page.
For your PDF problem try to use a IFrame.