Here "heart" is a metonym for "mind." The phrase "it came into his heart" is an idiom that means to decide something. AT: "it came into his mind" or "he decided" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-idiom]])
This refers to his people, and not just to his family. AT: "see how his own people, the children of Israel, were doing" (See: [[rc://en/ta/man/translate/figs-explicit]])
# Seeing an Israelite being mistreated ... the Egyptian
This can be stated in active form by rearranging the order. AT: "Seeing an Egyptian mistreating an Israelite, Moses defended and avenged the Israelite by striking the Egyptian who was oppressing him" (See: [[rc://en/ta/man/translate/figs-activepassive]])
Here "hand" refers to the actions of Moses. AT: "was rescuing them through what Moses was doing" or "was using the actions of Moses to rescue them" (See: [[rc://en/ta/man/translate/figs-metonymy]])