OP, let me attempt to simplify this for you.
Despite your contradictory statements e.g. references to 'your parents' address, which is where you live permanently, and Enceladus' attempt to get a straight answer to whether you received a NTO which you responded to by showing docs issued by the council (issuing and service being different) etc. now that we've seen the NTO and the council's PCN timeline IMO this case is essentially very simple.
The council's PCN timeline evidence shows:
An entry to the effect that a NTO was dated and posted 25 Oct.
An entry to the effect that another NTO was produced, dated and posted on 26 Oct. (which in law was deemed served Mon. 30th and which in law prevented the authority from applying the surcharge until 27 Nov.)(and which was unlawful if indeed they'd issued another on 25th)
An entry to the effect that a CC was produced dated and posted on 27 Nov.
An entry showing payment of £70 received 27Nov.
An entry showing a CC posted 27th Nov.
A separate response to you stating payment made 26 Nov.
Even shorter version:
CC issued 27 Nov. Served 29th on which date and on which date ONLY you were liable for the increased penalty. You are NOT liable simply because a 28-day target was exceeded, this only permits them to serve a CC.
Write to the morons and set out your conditions for not going public with their stupidity and unlawful actions:
1. Cancel PCN;
2. Apology;
3. An undertaking to review their procedures.
Wait for others.