What is the ruling on a teacher seeing the 'awrah of his female student at the student's request to prove that she has engaged in masturbation, and what should the teacher do to feel God's forgiveness?

As long as you have repented to Allah from looking unlawfully at the student's 'awrah, then there is nothing upon you. You are not required to seek the father's forgiveness or inform him of what happened. You must conceal yourself and not tell anyone about your sin. Repentance is accepted, and the one who repents from a sin is like one who has no sin. So, do not pay attention to whispers [of Shaytan].