Ho do you create shadows?

convert to black by selecting black as your active color and filling in your duplicate with that (I usually use ctrl click on the layer to select it then alt+backspace to fill).

by fade I basically meant adjust transparency/alpha, and that can be done in the layer panel. But, if you want, you can make a gradated blend, of either or both the transparency and blur (blur coming from a filter of course and gaus is pretty typical)