Adding a second wordpress blog as a subdirectory

Can anyone help me install two subdirectories to my wordpress site for these different purposes…

1. One would automatically show one category’s posts from the main site without having to double-enter any copy or layout elements, but be able to have different sidebar or menu content than the main site. For example, tv.mainsite.com would pull all the posts from http://www.mainsite.com/category/tv.

2. Another would have the same sidebars and menus, but unique posts not found on the main site.

Any ideas?

My site is http://www.publicmediaservice.org if that helps answer any questions.