Why is she such an idiot and how do I deal with her?

Who gives a flying f*** what she thinks or say? If you want to listen to some music on your headphones, by all means, do so. She has no rights to tell you how the place should be. She's probably gonna flunk and be left behind anyway, so hopefully you'll get a new roommate soon. I know it sucks to have bad roommates, but focus all your energy on your work and don't care too much about the rest.