You cannot appeal the result.
You will always have a second series pass.
You can only appeal the conduct.
It takes a couple of months as an appeal board is held which is mainly ran by the CAA legal department.
Since it is a legal matter I would encourage you to stay well clear of posting a thread like this. I suggest you do not give more information on this forum regarding this issue.
Honestly, from what information you have given you don't seem to have a strong case, and your chances are slim.
However, the examiner is required to inform you of the appeals procedure, and you have 14 days I believe in which to appeal. If it is past this you cannot appeal.
The school shouldn't really be involved other than to show you the regulation. The appeal has to come from the applicant, not the school, and it is between the applicant and the CAA. The school shouldn't get involved unless the CAA request so.