Is it permissible to convert a personal Facebook page into a public page (for males and females) with the aim of Da‘wah (Islamic proselytizing) and advice, while blocking private messages from women and only responding to their public comments to discuss issues such as immodest display (tabarruj) and illicit relationships?

Thank you for your desire to spread knowledge to educate people about their religion and to advise them. Indeed, spreading knowledge with wisdom and good admonition is the function of prophets and righteous callers to Islam. Alerting women to violations is part of enjoining good and forbidding evil, with the necessity of adhering to the legitimate Islamic guidelines when dealing with them, and establishing controls that prevent forbidden acts.