Is there any way i can get a page of posts from a certain category to look like the homepage (twentyeleven theme) of just blog posts?
WordPress creates archive pages for categories. Using the Twenty Eleven demo, see this URL: http://twentyelevendemo.wordpress.com/category/uncategorized/
Its actually really simple to do. In the 'Appearance' tab of the left had admin sidebar click 'Menu' Once in menu you'll see a block called 'Categories' click the check box of the catagory you want to appear on a page, then click 'Add to Menu'
Go to your home page and you'll see that you have a new menu item that links to a page of post from that particular category.
Hope that helps.