How can the girl's family be informed about getting to know her for the purpose of engagement, and is it permissible to seek the help of another girl as an intermediary to appease the family?

Facilitate your matter and communicate with the girl you wish to marry through a trusted sister or female relative, so you can get to know the girl and inform her family of your intention. One benefit of this is that she can tell you about her beauty. Do not forget the legal gaze (An-Nadhra Ash-Shar'iyyah), and consult trustworthy individuals who have interacted with the girl, along with the importance of performing Salatul-Istikharah (the prayer for guidance).