http://www.minibb.com/forums and are very different settings. http://www.minibb.com/forums points to your forums folder (without slash), and stands for the name of the index file. should not contain URL path - it's just a file name (or blank string).
There may be different start names for your board: index.html, index.php, start.html and so on. is for such issues when the board has something specific or hosting-related. In most cases, when you have index.php as the board's primary file, and if your server is configured to support the index file without specifying its original name (like it could be done in Apache), you may just leave this variable blank. Then all navigation links across forums will point to a "blank" index ending with the slash. It's like on our forums here.
I can't tell anything regarding logged status - but it's definitely a cookie issue, most probably it appears because of that
- domains without 'www' and with 'www' are different things
, for miniBB you should have only one, with or without 'www'.