Thanks for help. The reason why I wanted WP in separate directory, is that I was not sure how to redirect old HTML pages to their new equivalent (to keep rankings, etc). I was going to use redirect plugin to do that. I thought with old site installed, I could update the redirects one-by-one and test.
Still working on issue. Really weird results. I moved some old site file out of public_html, yet my browser still finds them afterwards. Even with cleared cache. Maybe I created some kinda circular reference in my .htaccess files in root and wordpress bw directories.