What is the religious ruling on a girl loving a young man when her family refuses his proposal now due to his studies, knowing that she fears God's displeasure and that she prayed Istikhara and her attachment to him increased, and she realizes that her mingling with him is forbidden?

You must sever the unlawful relationship and repent to Allah Almighty. If the young man wishes to propose to you, then let him approach the matter through its proper channels and propose to you through your guardian, and let him عقد عليك (perform the marriage contract with you) a legitimate Islamic marriage contract. You both can postpone the wedding or wait for it until he completes his studies. The validity of the marriage does not depend on the approval of his family, though it is preferable.

Performing Istikhara (prayer for guidance) regarding accepting or rejecting the young man is commendable. A feeling of openness and ease in the heart thereafter is an indication to proceed. Dreams can be used for reassurance but should not be relied upon. It is not permissible to perform Istikhara for the continuation of an unlawful relationship.