No shoes just socks....well I guess it DOES depend on the person yeah know? So IF you WANT to wear shoes under your rain boots go right ahead! ;) But if your gonna do that then yes I would buy a size up (but first try on! (so that you know if you should go up another size or not))
Yes, you wear rain boots over shoes. When buying rain boots, choose those that are one size larger than your normal shoe size. This will make your legs appear slim and attractive because of the extra room towards the top of the boots.
historically, you would wear a waterproof rainboot called overshoes over your shoes (duh!) rainboots are like shoes. . . you should wear them with socks. i don't think they even sell overshoes any more.