The easing on your Position and x Rotation keyframes is different for each box layer, so they move and rotate at different speeds. Highlight all the keyframes on both layers, hold the command key and click one of them. This will convert them to linear keyframes. Then if you want to ease part of the animation, make sure you apply the same movement to both layers.
I'm guessing you need to push your white background layer back in z space. You won't see shadows if it's on the same plane as the other layers. Also make sure the Accept Shadows property is on for that layer.