Can you give me a step by step way to recreate what you're seeing (along with DNN version, provider version if not the standard DNN provider,etc. )? I just logged into one of the portals I host with a general user, went to a page that only Registered Users have access to, went to another page, logged out and then clicked on back and wasn't logged in and had to re-login to see the content.
Or did you mean when a person is logged into a DNN site, leaves the site without logging out, and then goes back?
As for your second question, I haven't looked at the .ascx page but it may be possible to just change the layout of the page without having to change any of the code.
And for your third, good question. Without a post-back of some sort after they enter values in the fields in the first place it would be pretty difficult to populate the second text boxes.