What are the limits of my authority and influence over my 15-year-old sister, who is communicating with a man of bad character, who does not pray, and is an addict, knowing that she herself does not pray, wears immodest clothes, and behaves disrespectfully, and how can I deal with this situation effectively, and is it permissible for me to delete their conversations?

You must enjoin your sister to do good and forbid her from evil. You are not permitted to remain silent regarding her objectionable actions. You must prevent her from committing sins and from facilitating corruption for herself, while advising her gently and warning her of the consequences of those objectionable actions, especially negligence in prayer, disobedience to her mother, and unlawful relationships. You should encourage her to repent, help her learn the rulings of Islamic law, and strive for what strengthens her connection with her Lord. You do not have the right to access the young man's account to delete the messages.