Hi
I think the first problem you are encountering is a core concept of Joomla - it works based on menu links
These menu links control how content displays e.g. module assignment and how content is loaded
Essentially for a module to load correctly a menu link has to exist - it doesn't have to display on a site but it needs to exist on the system
e.g in your example create a new menu and call i hidden - then add either indivdual links to k2 items or a category link that includes in the category items you want to load