What should I do about my cousin whom I saw committing indecency and harassment in his youth, and he has shown no signs of repentance, knowing that I have informed my father and another person about the matter, and I do not feel safe in his presence?

If a man of religion and good character proposes to your sister, you should agree to him, based on the hadith (definition): "If someone whose religion and character you approve of comes to you, then marry [your daughter or female ward] to him. If you do not do so, there will be tribulation on earth and widespread corruption." No one is held accountable for the sin of another, for every soul is pledged for what it has earned. His brother's action is heinous; if he is abandoning prayer, his crime is even greater, and he must repent. Your seeing him from a crack in the door, if it was not intentional, then there is no blame on you. But if you intended it, then it is spying, which is forbidden. Informing others that he committed indecency may amount to slander (qadhf), which is a major sin.