That reply is unlikely to have helped things, editing a screenshot to remove the discount marker isn't an "honest mistake", and a 16-17 discounted ticket isn't valid with a family and friends Railcard (as you obviously knew, because you tried to hide the discount).
I'm not sure you need to research ticketing policies to understand how you did something wrong either.
I would write another letter, actually taking accountability for the conscious actions you made to defraud them if the fare due and post it here for suggestions before sending to Northern on Monday. That's the only way you're going to avoid court.
kindly find below letter i intend to send on Monday
Subject: A Heartfelt Plea for Mercy and Forgiveness
Dear Revenue Enforcement Delivery Manager,
I am writing this email with a heavy heart, overwhelmed by regret and sorrow for my actions on 30 September 2024. I cannot begin to express how deeply ashamed and devastated I am. From the bottom of my heart, I am so, so sorry. Every single day since that moment, I have been consumed by guilt, unable to find peace, knowing that I made a terrible and inexcusable action.
I take full responsibility for what happened. There is no justification for my actions, and I will forever regret that I allowed myself to make such a foolish decision. I have let myself down, and the thought that I may have jeopardized my entire future because of this fills me with unbearable fear and despair.
This situation has weighed so heavily on me .The fear of how this might impact my life and the shame from my actions has left me completely broken.
Since that day, I have done everything possible to make sure I never, ever take such action again. I have followed every rule, bought every ticket correctly, and ensured I fully understand the regulations.I have not committed any offense before and I have learned a painful and unforgettable lesson.
I try to be honest as possible as a diligent chemistry teacher. I made a terrible decision in a moment of weakness, but this is not who I am. I would never dream of putting myself in this situation again. Please, I am begging you, with every ounce of sincerity in my heart, to show me compassion. Please, I am pleading for a chance to make this right without it destroying my future.
I am willing to do whatever it takes to resolve this pay any fine, make any repayment, comply with any conditions. Please, I ask for your mercy. If there is any way to settle this matter outside of court, I would be forever grateful.
I know that I do not deserve your forgiveness, but I am humbly asking for it. I will never take this second chance for granted if you give it to me. Please, I am desperately hoping for your kindness to settle of of court.
Thank you for your time.