Another difference between over and above is how literarely it is. Over is actually directly above. For example the lamp over you. and the umbrella over you. where above is more vague about exactely the position of the thing you are referring to is. the stars above you. or the plain flew above the clouds. (which clouds? where? is vague.)
I hope this answered your question a bit better. The other one has already been asnwered.
cheers