Does the repentance of a young man who molested his female relatives in his youth get accepted, and can he redress the injustices that befell them and his family, knowing that people like him are threatened with severe punishment in this world and the hereafter?

You should increase your seeking of forgiveness (Istighfar) and good deeds, and distance yourself from the causes of sin. The door of repentance is open, no matter how great the sin. Allah Almighty accepts repentance from His servants and forgives all sins, and repentance nullifies what came before it. As for redressing grievances, you should supplicate and seek forgiveness for those you have wronged.