>If you want to build a small web app prototype (for use on smaller screens, e.g. iPad mini) can you do it with just VS 2012 Web Forms? Or you need a different tool? (At this point I only want to build a UI and later bind it to the database).

You could - but probably shouldn't. Craig pointed out the Mobile template option with MVC 4. That gives you a bunch of ready built jquery styles and a .js file which gives a big start towards a mobile friendly UI. If you use the template you can still use standard aspx pages rather than cshtml if you want. But you will still probably find MVC useful with those as well....