Is a sister's prayer to be engaged to the same young man the questioner intends to be engaged to considered a transgressing prayer? Does it have any bearing on the difficulty of the questioner's engagement? And what should she do about it?

It is better for the supplication for marriage to a specific person to be qualified with "if that is good for me," because Allah Almighty knows best what is good. It is also better to supplicate generally for a righteous spouse. As for the sisters supplicating for marriage to the same person, there is no harm in it, if it is qualified with goodness, and it is not considered an unlawful competition as long as the goal is chastity and association with the righteous. One must beware of becoming attached to non-mahram men and of envy and jealousy among sisters.