Must this dream come true? Does it indicate that the dreamer must marry the girl mentioned in it? And what should he do?

A dream is merely one of the glad tidings that one can feel reassured by; it is not a source for receiving rulings, nor can any matter of religion or worldly affairs be built upon it. Moreover, its realization cannot be definitively asserted, as it pertains to knowledge of the unseen. The dream of a believer is mostly truthful if the time draws near, but the predominance of truthfulness does not negate the possibility of falsehood. Therefore, if the girl is religious and not engaged, then rely on Allah and propose to her.