I can't help with the material - waiting to see what Snarly has to say on the subject - but regarding your concerns on the shadow:

If I've understood you correctly, your light source has a large area so it will naturally produce very blurred shadows for objects which aren't close to the 'frosted' screen. Although this isn't my area of expertise I don't imagine there's a way to change this - the renderer is doing the 'right' thing from a light physics point of view.

If this were my project I might experiment with a spotlight behind the figure, where I could adjust the shadow blur.