What is the ruling on the dowry agreed upon between the two fiancés, which was paid to cover travel expenses and the cost of obtaining residency permits, with the remainder intended for purchasing gold, in the event that the engagement is dissolved before the marriage contract?

The woman is not entitled to any of the Mahr as long as you have not contracted the marriage with her. She must return whatever she has received from it. As for what the woman spent from her own money for your benefit with your permission (such as processing documents), that is a debt owed by her to you.