Is it permissible to supplicate with the words: "O Allah, whoever You have loved in You in this world, make her exclusively mine on the Day of Resurrection" for a girl one has loved for Allah's sake and wishes to marry?

It is permissible to supplicate for the one you love to be your wife, as long as she is not married, while being careful not to go to excess in that, lest your interests be neglected. However, if she is married, it is not permissible to supplicate for that, because it is considered an aggression in supplication.