having just gone through all this myself i’m now quite familiar with it all. Being the one who had the work done mind. The party wall award is paid for by the person doing the work. (its usually around £500 per party)
Make sure that when the award is complete and you receive all descriptions/photos of any current issues with your side of the wall that you talk to your neighbour before work starts – they may be able to resolve them with little/no cost to you as the work is carried out.
Its worth doing as it covers all issues that may occur when the building starts – if a neighbour claims a crack appears during/after works done – the award will show if this is indeed true or not, if true then this will need to be fixed at cost of the one doing the building work
You can appoint you own surveyor – you dont have to use the same one that he is using – but at the end of the day they work for the crown and not for you or him, so it doesnt really matter.
The award should also cover when the builders can and cannot work (i.e. sociable hours) and what access may be required to your property if any – in which case what notice is required to be given
when the works are being carried out a building inspector should make frequent visits so if its looks dodgy – they can stop the build (usually it wouldnt get that far as the tech drawings that the surveyors produce are sent to the council first and need to be signed off as safe and viable)