How do they get the cranes and counterweights down off the top of buildings when finished?
The cranes and counterweights aren't on top of the building. They are on the ground constructed with structural steel supports.
Dereks, which are built along side of the buildings, actually take themselves apart. There is a jacking system which attaches to the segment that is 2nd from the top. This lifts the bussiness end of the crane off the top segment which can then be unfastened and lowered to the ground. The jacking system then replaces the crane on the new top, travels down one more segement and the process is repeated. It is actually cool to watch.
sometimes they dont. i have heard of buildings where they left the crane body as the structure for the elevator