what exactly caused it to stop when it found the right settings?
To use the bombe, you had to prepare a "menu" which consisted, essentially, of things called "cribs," which were phrases or words that you had a hunch would be in the message you were decrypting, based on past experience. That is how the bombe always worked, and the breakthough moment in the movie was a bit misleading because you would have to wonder what was the bombe doing before Turing and company started looking for "heil hitler" or "weather report."
The bombe stopped when it encountered a startup setting that resulted in the crib being found, but many possible settings might do that so there were typically many "stops". After each stop, they would have to enter those settings in the real Enigma machine and see if the entire message made sense; usually it didn't, so they would restart the bombe and keep looking.
Helen's German counterpart starts his messages with CILLY, is that the encrypted message or decrypted?
The CILLY thing with Helen was a combination of fact and fiction. Helen would not have known the actual translation of the letters she recorded via Morse code. German Enigma operators were instructed to use random patterns at the beginning of each message where they entered the message key, but sometimes operators used the same key each day. The key was either 3 or 4 letters, depending upon how many rotors were used (Army and Air Force used 3, Navy used 4). The key procedures changed over time.
Read "Seizing the Enigma" by David Kahn, it is the best resource on Enigma I have found.
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