Bols
1. I believe the Def Sec can do this but the Sheriff can also re-open the FAI.
The HoL and PAC I'm not sure about but it would save everyone trouble if the MoD decreed 'CNPD'.
2. Dunno - too many interested parties - Boeing, Textron Lycoming, BAe (who now own Hawker Siddeley Dynamics), the Gov't and MoD, Retired Offs various and, not least, the families of the crew and the pax!
3. IIRC - Pilot Error, Engineering Error, Normal Operating Hazard, Cause Not Positively Determined - I can't remember if there is one for 'Design Fault'. In view of the outcome of the Glen Ogle Tornado (with much more technical data), CNPD is the only one that fits.
4. I cannot speak for the families but, for me, the answer to your question is a resounding 'NO'. One cannot prove nor disprove any error on the part of the crew. As they are deceased and there was no CVR nor ADR, the only reasonable outcome is CNPD. Which is what the original BoI was trying to say!