The paratroop scene airplane is a Junkers Ju 52 (I'm not sure of which model, though).
Looks like Messerschmitt Bf 109s are used at one point on the ground.
The helicopter is apparently: "The helicopter is a modified Bell 47-G with Bell-Hiller mixing and a flybar for the control system. Easy to fly and very stable. Helicopters similar to this first came out in Germany in 1944-45. The Germans were 25-years ahead of the rest of the world in aerospace, resulting in OPERATION PAPERCLIP at the close of the war in 1945-46. Soon followed a HUGE leap in American jet and rocket science and technology. The best mathematischens were also German." per Beamshipcaptain on YouTube.
That's all the planes I could see using ready available internet footage.
Caleb Williams MSP AUS STL AMS CPH LGW YYZ