Mr Punter

Just keep shopping round. This firm https://www.kiteleys.co.uk/conveyancing-costs looks less than a grand.

You can have some transition pieces or a shallow ramp. What is the floor finish? Are you having a mat well?

I have known the foam to break down into a powder. EPS is OK but PIR I am less sure. Put them free to collector?

+1 and the DNO do not allow you to run electric through sewer pipe or non approved ducting.

3M do some that are fairly transparent for the reduction in solar gain but expensive. The silver reflective ones are cheap and effective but noticeably darker inside.

Your solicitors gave you good advice. Party Wall award will happen anyway, as will planning consent. I don't know how the freeholder consent works when you have a share in it, but they are often "not to be unreasonably withheld" or some such. Try to let it wash over you and do not deal with the neighbours directly or react to their provocations. Avoid words like "lies", "hate" and "nasty" as they are not helpful.

You will probably not get pulled up on this. They often allow a maximum 100mm leeway to work in with brickwork. If it already built you don't have much option. If not, just do as @DevilDamo suggests.

You could try another fabricator. They have over 30.

I don't understand where the pressure switch would fit in. It is normally float type switches for these applications.

Yes, start with a header one end and alternate with each course.

I have an investment property where access to the back garden can only be gained via a basement flat. It is a right pain at times.

If we assume that you have 30m3 of soil to excavate and remove, a micro excavator will make the digging easy. A week with a decent operator plus a labourer may do it. If you have space at the front, make up a large 4 sided enclosure from 18mm OSB and 4 x 2 to store the spoil ready for a grab lorry, or just pile it up. Wheelbarrow through the house. I would budget max £8k but you may get it done for half that.

The thin slithers of slate at the verge are poor but I assume he was reusing existing materials? Dry verge slate system and some barge boards needed.

If the render is solid I would leave it. Just scrape the flaking paint and repaint.

You could chase it into the brickwork.