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?
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.
WordPress creates archive pages for categories. Using the Twenty Eleven demo, see this URL: http://twentyelevendemo.wordpress.com/category/uncategorized/