Is sending an email to a young man to ask him about the possibility of proposing to her considered haram, knowing that they had a prior relationship and that she desires to marry him according to the Sunnah of Allah and His Messenger?

It is not permissible for a woman to correspond with a man who is a stranger to her, due to the great harms involved, even if the intention is marriage. If a woman desires to marry a specific man, she should send someone she trusts from her relatives to propose the marriage to him.