Mr Punter

Yes you will fill the gap between the rough edge and the extender.

Yes, the extenders are the way forward. Shame they were not fitted pre-plaster, but at least it gives something to fill to.

Your biggest challenge will be to get the concrete in the right place, as once it is poured you won't be moving it. If you can get the lorry near all the trenches, fantastic. If not you would do well with a concrete pump - either boom or line type. You will need minimum 3, preferably 4 people, plus the pump guy and concrete truck driver. Work out exactly what you are doing before anything turns up. How will the concrete lorries get in and out, traffic management etc. 6m is very wide to screed to. Can you get some pegs in the ground as levels? If there is a screed layer on top, the accuracy of the slab doesn't matter too much.

I have only done these in flats.

Not me. I would spec it on external render though.

As suggested by @ADLIan and @IanR, it is probably the thermal bridge calculations that are the issue. You are far better off using existing calcs than having custom ones. The default psi values are unbelievably negative and these are probably the ones that were used.

Bed joint reinforcement (the train track stuff) above and below the openings may have helped. I have only specified it on rendered walls or brickwork feature panels like stack bond. Mesh in the render also helps. You best option now is filler.

I saw these people the other day: https://anthonygold.co.uk/service/leaseholders-and-freeholders/conversion-to-freehold-enfranchisement/ May be worth another quote. Are the other leaseholders on board?

It looks nice and tidy. Did you concrete over a pipe there?

I know someone who used expanded clay fill, then concrete slab with UFH. It was a considerable depth. You will need a SE input obvs.

If the cavity does not need ventilation you could fit a DPC cavity tray around the base of the plinth bricks linked to the inner leaf and fit the mini weep vents at 900mm centres.

Well the good news is they haven't tried to cover it up. Get a full survey and report. Make sure it includes roof condition, timber condition, damp, dry rot and condition of brickwork.

So is this an insulated masonry cavity wall?

You need to confirm with the contractor that they will immediately spray the curing compound on the finished slab. If the water evaporates from the slab too quickly the concrete will not properly cure. That said, the house will not fall down.

If there is only 1 layer you will be fine with the overlaps. If you can get someone to help placement it would help a lot as the sheets are heavy and awkward. You may want some tie wire where the sheets join and allow for a 300-400mm overlap (40x wire size).