What is the ruling on one whose father sent him to give Zakat al-Fitr to an old woman, but he spent that money on himself, and how can he expiate for his mistake, given his regret for his action?

The one who betrays a trust and transgresses against charity is obligated to repent to Allah. Repentance is not valid unless the charity itself, or its value, or its equivalent, is returned to its rightful owner.