Is the speaker's statement: "Do as I do; I accumulate my sins until 'Arafah, and my sins will be forgiven" correct, and is the response to him: "And what makes you so sure you will live until the Day of 'Arafah?" correct?

What this person said is a terrible abomination. Death may overtake him before the day of Arafah, and he does not know if his fasting will be accepted. His insistence on forbidden gazes is among the major sins that require specific repentance. As for fasting on the day of Arafah, it only expiates minor sins. He must fear Allah, beware of sins, and reflect on the greatness of the One he disobeys.