What is the ruling on continuing an engagement to a dark-skinned girl, despite the suitor accepting her skin color, while his family rejects this color, and should he act upon the dream he had after the الاستخارة (istikharah) prayer?

Color is not a barrier to marriage if the woman is religious and of good character. You can marry her if the mother is convinced, otherwise her consent takes precedence. Choosing a woman based on color is not forbidden unless the motive is arrogance, for the most honorable among people are the most pious. It is important to note that this girl is a non-mahram, and it is not permissible to be alone with her or speak to her without legitimate Islamic guidelines. Ruyat (visions/dreams) do not establish rulings, and what is required is to perform istikhara and entrust the matter to Allah.