Jesus is speaking about himself in the third person. If necessary, you can translate this in the first person. (See: [[rc://en/ta/man/translate/figs-123person]])
This can be stated in active form. Alternate translation: "did not come so that other people would serve him" or "did not come so that other people would serve me" (See: [[rc://en/ta/man/translate/figs-activepassive]])
Jesus' life being a "ransom" is a metaphor for his being punished in order to set people free from being punished for their own sins. Alternate translation: "to give his life as a substitute for many" or "to give his life as a substitute to set many free" (See: [[rc://en/ta/man/translate/figs-metaphor]])
To give one's live is an idiom meaning to die voluntarily, usually in order to help others. Alternate translation: "to die" (See: [[rc://en/ta/man/translate/figs-idiom]])