Mr Punter

I have seen it done in hot bitumen. It looks quite an intimidating project.

You don't need to do anything. The only issue may be if you have parked cars in the road and the council become involved.

It may be better to have the rafter insulation extending full length of the rafters instead of insulating the dwarf walls and part of the ceilings below. 30mm of insulation under the rafters is also good and will help eliminate any condensation / damp potential.

If your written deadline has expired I suggest you issue proceedings for recovery of the £3,000 plus court fees. You can do this online, although it is a bit tedious. https://www.gov.uk/make-court-claim-for-money/make-claim

The topo looks OK. What is wrong with it? It looks like the site setout was wrong.

I am pretty sure there must be a lintel or beam above, otherwise they would not have been able to build the bricks across the top.

Something very strange here. Like @Canski says, survey should have included the neighbouring buildings. On the basis that the surrounding ground on the survey is about 100.00 and your FFL is 100.15, the blue lines are wrong if they are FFL. Maybe they are reduced dig levels or top of foundation or slab and you have insulation, screed and finishes on top?

190mm on one side only, so not exactly purge ventilation and not as much as a centre pivot on a slight pitch.

You can talk to you local councillor as they are able to "call in" applications. Parish councils don't normally have much authority and are consulted for comments only and do not make decisions on planning applications.

From what you have posted the issue is just down to the hinges on 2 or 3 rooflights on a flat roof. Why do you think the roof may have to come off? You probably don't need scaffolding. In my experience, the Velux flat roof windows do not offer much ventilation when open so you could consider ditching the opening function if push comes to shove. With the fixing the brackets through several layers of zinc, could you offset the hinges to overcome this? The legal route can be very long and costly and it sounds like it will be difficult to achieve a complete victory, while you risk considerable expense. You would need to expand on the "numerous potential defects". You would need actual defects to convince the court, even if they have not resulted in e.g. water ingress.

For sewers, unless this is a requisition, the work is normally carried out by a private contractor and paid for by the client.

That is poor. I thought PAS24 was supposed to prevent this type of thing. I would ask the supplier and their accreditation company to give their view on why the window failed and what should be done for future.

Be very careful when applying the scrubbable emulsion top coat. If you get any roller spray it will not come off once dried.

The outside air will likely be drier and colder than the inside air, so no real risk of condensation.

For timber fence posts my mate digs a 30" deep hole, so 750 deep. For your gates, the extra 450mm sounds good. Make sure the ground is nice and stable. If it is crappy made ground you could go deeper. You will already have a hole where the failed posts were, so you know that you will need to make the new ones bigger and better. Can you fix to the building either side, or is that a no-no? If you are allowed, get some angle drilled and welded on before you get this galved. Resin fix to the buildings.

It will be down to ground conditions. You may need to mess around with a bit of hand digging and some shuttering around the services. I would go 800 x 800. It is no fun digging out a post that has failed.

All the pipework to and from the plenum boxes, as well as the boxes themselves, should be insulated.

I have seen this sort of setup with a welded steel u shape, like a goal post but inverted so the crossbar is in the ground.

That is quite often a weak point. It sometimes gets filled with mineral wool but there is a risk that too much can be added, closing off airflow beneath the roof tiles. I think your issues are mostly be reveals, external thresholds and dot and dabbed plasterboard. If you drill small holes every 200mm around the top of the walls you could squirt in some expanding foam. Along the bottom, remove the skirting board, foam the gap and replace.

Can this not be done from the inside? I doubt they will even need to cut many tiles. They may need new flashing but I suspect the current ones can be reused.

It is sometimes simpler to have the basement the same footprint as the floor above. Make sure it is deep enough. Low headroom could be a bit oppressive. Get it priced up before you get too carried away. Even if it is not a cinema, it could be used as a bar, games room, disco, sex dungeon etc.

Looks like the black bit is meant to friction fit. Failing that, a bead of decorators caulk around the rim of the white bit will hold it securely to the plaster. You can always cut round it later if you need to remove it for any reason.

I imagine the other outside taps are teed off the mains supply. There is often a meter or stopcock in the ground near the site boundary.

A drawing would make more sense here. The breather paper for the SIP needs to direct any moisture away from the structure.

Be very careful with fire test claims. Grenfell passed. Class E reaction to fire I think means it is normally flammable. I think it would be best if a professional specified this and get it cleared with Building Control.