Is a young man considered a pimp (dayyūth) if he overlooks his unmarried sister talking to people online within the bounds of decency, and what should he do, and is his repentance accepted if he was a pimp, and is the pimp the woman's guardian or her brother?

A 'dayyuth' is a man who lacks jealousy over his family and those he is forbidden to marry (mahārim). The abandonment of jealousy is a blameworthy 'dayāthah' (lack of protective jealousy) both in Islamic law and by natural disposition. Therefore, the guardian of a woman must prevent her from actions that lead to her interaction with men without a legitimate Shariah interest. If the guardian falls short, then her brothers must prevent her. If she does not stop, they should continue to advise her, and by doing so, they will be absolved from the threat against the 'dayyuth' mentioned in the hadith (definition): "There are three whom Allah, the Mighty and Majestic, will not look at on the Day of Resurrection: the one who disobeys his parents, the woman who imitates men, and the 'dayyuth'." As for the repentance of the 'dayyuth', yes, it is accepted, for Allah forgives all sins for those who repent.