What is the ruling on getting to know a girl with the intention of proposing to her by speaking with her in the presence of her brother, without the knowledge of her family?

There is no harm in a man speaking with his fiancée or with the woman he intends to propose to and see, provided one of her mahrams (unmarriageable kin) is present, even if her guardian is unaware. However, this must be limited to what is necessary.