Some lenders won't lend on properties with flying freeholds. Therefore they may ask you to repay the loan in a worst case scenario.
If you are keeping the properties for the long term and are happy to renew the mortgage deal with Birmingham Midshires then you probably don't need to rock the boat until you are financially able to repay the loan if required
There have been situations recently of private inspection firms going bust, then having to revert to LABC anyway.
Personally I have used both and happy with either. LABC probably do more jobs so more likely to know your ground conditions etc if that might be an issue
Way easier to hire a digger+driver combo. When you look at hire prices you are basically paying a £100 a day for the driver. Look on Facebook marketplace etc.
As the driver will know their machine inside and out they will get that dug out and footings dug in a week or less
Is the block wall on your property? If so that may make a difference.
Start by asking the neighbors they might appreciate the privacy and then you could just go ahead without worrying about planning permission
Who does the wall on the boundary belong to? If it is your wall then you would be liable for damage on your own wall, so I would just wing it without a PWA.
Your neighbour is 100% right.
You should deal with the water coming off your own roof with guttering on your own land.
The advice of a good roofer should help
Powder adhesive is for wall and floor tiles. Ready mix adhesive is for DIY.
This sounds like 100% user error, but without seeing what has happened I can't tell you what you did wrong!