Is it permissible to pray that no other woman supplicates to marry a specific man? And what should you do for Allah to be pleased with you and grant him to you?

It is permissible to supplicate to Allah for marriage to a specific person, and there is no need for excessive anxiety or fear. Allah's pleasure is achieved through faith and piety, and it is not necessarily contingent on the fulfillment of a request to marry a specific person. Indeed, Allah's turning that person away from you might be a manifestation of His pleasure, for He knows best what is most beneficial for His servant. Therefore, ask Allah to ordain what is good for you and entrust the matter to Him. Give thanks to Allah if it materializes, and if He turns it away from you, know that He, glorified be He, knows what is best for you. Remember His words: "And perhaps you dislike a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows, while you know not."