All residence hall bathrooms are equipped with shower curtains. If you so desire, you are permitted to put your own up, but the original does need to be in the room when you move out. From my experience, the shower curtains are in great shape; they are often replaced annually.
Regarding bath mats – in Warren, you almost definitely need to bring your own. Some halls with floor baths may have rubber mats to prevent slipping on the larger surfaces, but I’m not certain on that either.