No, you do not need to download previous Core Updates. The links for them are probably deleted anyhow.
The latest Core Update patch includes the changes of previous Core Update patches. However, Core Update only covers the Spitfire/P-40/Mustang trilogy. If you have the Accu-Sim P-47, B-17, Piper Cub or Stratocruiser you'll have to follow the specific patching instructions for each of those aircraft.
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