1. They have not re-offered the discount, therefore you're on the hook for the full penalty.
2. You register your appeal. Simply follow the instructions and register. You rely upon your formal representations and procedural improprieties arising from the Notice of Rejection. You do not need to go into detail at this stage.
The letter is signed by someone or something, it's indecipherable. It says:
*******
Kingston Parking Services
Which means that they are employed by Kingston Parking Services, not ***** on behalf of.
Not only are there issues regarding authorisation as regards officers, this also applies from the Secretary of State's Statutory Guidance:
The process of considering challenges, representations and defence of appeals is a legal process that requires officers dealing with these aspects to be trained in the relevant legislation and how to apply it. They should be well versed in the collection, interpretation and consideration of the evidence, writing clear but concise case-specific responses to challenges, enquiries and representations, presenting the authority’s case to adjudicators.
Formal representations
Many enforcement authorities contract out on-street and car park enforcement and the consideration of informal representations. Enforcement authorities should not contract out the consideration of formal representations. Enforcement authorities remain responsible for the whole process, whether they contract out part of it or not, and should ensure that a sufficient number of suitably trained and authorised officers are available to decide representations of their merits in a timely and professional manner.
The authority’s standing orders should be specific as to which officers have the authority to cancel penalty charge notices. There should also be a clear audit trail of decisions taken with reasons for those decisions