Free Traffic Legal Advice

The link to the Westminster website I see from your post repeats what it says on the PCN, namely "01 -parked in a restricted street during prescribed hours". Any sign on a bay nearby does not apply to yellow lines.

You say he parked on a yellow line but there were no signs giving the restricted hours. This means he parked within a Controlled Parking Zone where the restricted days and hours are shown on sign at the entrance to the zone. A 2-minute look on the Westminster website shows he was parked within Zone A2
Restricted hours are: -
Mon-Fri 8.30am - 6.30pm
Sat 8.30am - 1.30pm

He would have passed these signs: -
https://maps.app.goo.gl/LoWEdsoPyN1ausLN6
I suggest he traces his route using GSV Street View, and at the point where he entered the zone, if the signs are not there he has a case.
Here is the location where he parked: -
https://maps.app.goo.gl/LoWEdsoPyN1ausLN6

So, the bottom line is the PCN seems to have been correctly served, unless the CPZ entry signs on his approach are missing.

I'm afraid not. Have you looked at the Westminster CPZ map ? They are large and whilst the guidance years ago saids they should not cover more than a few streets, that has been totally ignored for at least 20 years. It's just part of living in London. No sign by the yellow line = you are in a CPZ.

the is the only PCN we have.

and for the date, is it 14 working days - so should be 16/1 instead of 13/1?

I would wait for the NtO assuming they reoffer the discount if reps. are rejected.