Concerning the PCN and towaway. I assume you had to pay £240 release the car from the impound yard? Or was it £265?
Anyway at the time the yard should have given you a payment receipt, the PCN and a "Representations" form with instructions on how to challenge the PCN & removal and the deadline to do so. Sounds like you didn't do anything.
In case this happens again please be aware that it was a mistake not to challenge the PCN. Where a towaway is involved then always challenge and then appeal to the Adjudicator. You have no further financial risk in doing so and if you win then the £240 or £265 would be refunded.
As things stand there is no further remedy available to you. More than six months have elapsed since the contravention so I very much doubt that the Council will agree to any request to re-open the case, on the grounds that the process was not clear to you.
See does anyone else care to comment. Maybe it is worth asking the Council to consider a late representation?
For PCN PN21057693 it looks like you have an on-site PCN followed up with a posted Notice to Owner. It seems that somebody challenged the NTO by submitting a formal representation. Strictly speaking this should have been the Registered Keeper or a representative with written permission.
Anyway the Council did consider the representation/challenge and responded with a Notice of Rejection. The NoR provided details on how to appeal the matter to the Independent Adjudicator at the London Tribunals but it seems that you didn't do so.
Your right to appeal to the Adjudicator expired on Sunday the 23rd Feb. Since the PCN was still not paid a Charge Certificate was served followed by an Order for Recovery (of unpaid penalty charge). An OfR is a form of court order and cannot be ignored or the matter will escalate to bailiff enforcement and a £75 fee added, plus a further £235 if their initial notice is not paid.
Any attempt to appeal to the Adjudicator would now be over two months late, which is a pity because the evidence photos support your version of events. The evidence photos show different tyre valve positions, suggesting that the car was moved in between the initial observation and the PCN. And also this was a lower level contravention, towing your car in addition to the PCN was disproportionate.
The deadline to pay the OfR at £130 is the 16th May. Perhaps it is worth trying to lodge a late appeal with the Adjudicator, if you can make some sort of case that you were mislead as to the process.