Can you provide a little more explanation about what exactly it is you're trying to do?
When you say you want to include something like "css/header.php?page=index", what are you trying to accomplish? Basically, you are trying to perform a file include function (perhaps include_once()) on a URL. That won't work, as the previous poster pointed out.
It sounds to me like you're overcomplicating this, too. Is your header.php file supposed to output different HTML content depending on whether or not the user is on the "index" page?