Is it permissible for a person to pray to Allah Almighty for marriage to a girl who rejected him, and does that affect his provision in marriage?

Your supplication contains no sharia violation or harm to you; rather, it is good and among the most beloved acts of worship. It is not a condition for a supplication to be accepted that the desired outcome be immediately realized. Allah may hasten the fulfillment of the supplication, or save it for the Hereafter, or avert some evil by it, as stated in the hadith: "There is no Muslim who supplicates with a supplication in which there is no sin or severing of kinship ties, but Allah will grant him one of three things: either his supplication will be hastened for him, or it will be stored for him in the Hereafter, or evil similar to what he supplicated for will be averted from him." Have a good opinion of Allah and supplicate often, and know that what Allah has decreed will come to pass. He, glorified be He, knows what is good, as He Almighty said: "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."