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No code talkers were captured. There was a Navajo man who was captured by the Japanese in the Bataan Death March group. They interrogated him. He could not give them the code because he had not been trained in the code. He may have been able to figure it out if they Japanese had not tortured him.
Eichmann was captured on 11 May 1960 in a Buenos Aires suburb, he was tried, convicted, sentenced and executed.
The code breakers made a major contribution to the Allied war effort when they broke many of the Enigma Codes. They certainly aided in Germany's defeat more than most WW2 battles.
The Nazi Germans defeated the Canadians/Brits and captured many Canadians. See the links below for more details.
Actually the Germans did not think that the Enigma could not be broken, in fact they made many changes to the machine and the procedures for its use during the war to make it harder to break, just in case the enemy was making any progress at breaking it. However they did make the mistake of assuming that its encryption algorithm had no major weaknesses (the Poles and British found several) and that the very high number of combinations possible on the machine would make any cryptanalytic attack even if successful take so long that the information obtained would have no military value by the time a message was deciphered by the enemy (the Poles and British and Americans built large high speed parallel electromechanical machines called Bombes that automated this and could try hundreds of combinations per minute to reduce this time). The British also discovered that in practice many German Army Enigma operators frequently deliberately violated the official operating procedures, making their messages nearly trivial to break in some cases! German Navy Enigma operators were never allowed to violate official operating procedures, making their slightly different Enigma machine harder to break. Also even when the Navy Enigma was broken all you got was codewords which were gibberish without the current Navy codebook, making it necessary for the British to capture one every time the Germans replaced their codebook with a new version, until then no Navy Enigma messages could be read even when they had been broken.