Here are a few New Testament verses that address your questions. See more at scripturecatholic.com/apostolic_succession.html
Luke 10:16 - Jesus tells His apostles, “he who hears you, hears Me.” When we hear the bishops’ teaching on the faith, we hear Christ Himself.
Luke 22:29 - the Father gives the kingdom to the Son, and the Son gives the kingdom to the apostles. The gift is transferred from the Father to the Son to the apostles.
Col 1:25 - Paul calls his position a divine “office.” An office has successors. It does not terminate at death. Or it’s not an office. See also Heb. 7:23 – an office continues with another successor after the previous office-holder’s death.
1 Tim. 3:1 - Paul uses the word “episcopoi” (bishop) which requires an office. Everyone understood that Paul’s use of episcopoi and office meant it would carry on after his death by those who would succeed him.
Matt. 16:18 - no matter how sinful its members conduct themselves, Jesus promised that the gates of death will never prevail against the Church.
Matt. 23:2-3 - the Jewish people would have always understood the difference between a person’s sinfulness and his teaching authority. We see that the sinfulness of the Pharisees does not minimize their teaching authority. They occupy the “cathedra” of Moses.
Matt. 26:70-72; Mark 14:68-70; Luke 22:57; John 18:25-27 - Peter denied Christ three times, yet he was chosen to be the leader of the Church, and taught and wrote infallibly.
Mark 14:45 - Judas was unfaithful by betraying Jesus. But his apostolic office was preserved and this did not weaken the Church.
I hope that helps.