What is the ruling on loving a righteous person with a desire to be with them and hold their hand, and is it permissible to supplicate for their admission to the university?

If your love for someone is due to their uprightness and religiosity, you will be rewarded for this love, as it is one of the best acts of drawing closer to Allah. This is based on the saying of the Prophet, peace and blessings be upon him: "There are three qualities, whoever has them, will taste the sweetness of faith: that Allah and His Messenger are more beloved to him than anything else; that he loves a person and does not love him except for the sake of Allah; and that he hates to return to disbelief after Allah has saved him from it, just as he hates to be thrown into the Fire." And also his saying: "The firmest handholds of faith are love and hate for the sake of Allah, the Mighty and Majestic." You can supplicate for him to be accepted into your university to strengthen this love and to cooperate in obedience to Allah.