The catapults of the Omaha class were different than those of other cruisers and I believe the three installed on Fletcher class destroyers were also of this type.
I will let Nautilus Models answer the catapult question:
http://nautilusmodels.com/CATAPULT.HTM
As far as the crane, this Navsource page shows the plan for the aircraft crane for the BB Massachusetts was "made applicable" specifically to that ship. Seems to imply a likely standard basic design which would then be adjusted to individual ships:
https://www.navsource.org/archives/01/57n.htm
HTH some
Considering WW2 USN used SOC-3s and OS2U seaplanes (with some Seamews and Seahawks ) were stern cranes and catapults standardized on each ship that carried observation aircraft?
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