This has become a long thread and the OP has my sympathy for the poor way they have been treated, and I note there are many regular forum members encouraging the OP to Appeal
However, I note the OP says they have recently come to the UK and is thus naturally unfamiliar with the UK railway system and its rules -
I suspect the most practical advice now for the OP is to focus on the form of wording the OP should use in submitting their appeal in a way that maximises the chance of success.
Perhaps
@zapper_09 can post a draft of any Appeal wording they wish to submit (and I think there may be a word limit perhaps?) people on the forum can help get the wording as good as it can be with any suggestions or edits.
The Appeal needs to be short, focussed and succinct in my view. Much of the info posted explaining about how the confusion has arisen (the way the the train concerned is only listed on screen to Poppleton, and why) will not need to be part of the Appeal wording I would think.