What are the deeds beloved to Allah Almighty that a woman can perform so that Allah may answer her prayer for marriage to a specific person, especially if she feels despair after that person became engaged to another?

Everything that occurs in the universe happens by Allah's decree and destiny, and it is good for the believer. What you dislike may be good for you, and what you love may be evil, for human knowledge is limited. Be patient with Allah's judgment, and supplicate frequently for Allah to compensate you with something better. Say: "Indeed we belong to Allah, and indeed to Him we will return. O Allah, reward me in my calamity and replace it for me with something better." There is no harm in supplicating for marriage to a specific person, but it is better to pray for a righteous spouse in general so that your heart does not become attached to a particular individual.