This is an idiom. AT: "When Peter became fully awake and alert" or "When Peter became aware that what had happened was real" (See: rc://en/ta/man/translate/figs-idiom)
"Delivered" here is a metaphor for "bring" or "brought." AT: "brought" (See: rc://en/ta/man/translate/figs-metaphor).
Here "the hand of Herod" refers to "Herod's hold" or "Herod's plans." AT: "brought me from the harm Herod had planned for me" (See: rc://en/ta/man/translate/figs-metonymy)
Here "the people of the Jews" probably referred mainly to the Jewish leaders. AT: "all that the Jewish leaders thought would happen to me" (See: rc://en/ta/man/translate/figs-synecdoche)
He became aware that God had rescued him.
John was also called Mark. This can be stated in active form. AT: "John, whom people also called Mark" (See: rc://en/ta/man/translate/figs-activepassive)