Is informing the young man's father that he took money from the woman considered an injustice to him, and is it considered forbidden for the woman if the young man takes a loan to pay off his debt?

The young man must repay the loan to your mother as long as he is solvent, whether the marriage takes place or not. The lender has the right to demand the loan at any time. Therefore, your mother is permitted to inform his father or take the matter to court. There is no injustice to the young man in this; rather, he is the unjust one if he delays in fulfilling the right while he is solvent. If the young man takes out an interest-based loan (riba) to repay the amount, he is committing a grave sin, but taking the money from him is not forbidden.