You generally go from the CU to the void under the 1st floor floor boards, then down to the 1st socket, back up again and along then down to the 2nd socket and so on for ground floor sockets. You do similarly for bedroom sockets only go up the wall.
Yes, otherwise every time you do a minor alteration to a circuit you would have to do a CU upgrade, which is not very practicable if you think about it.
To keep the costs down I would suggest let the electrician purchase what he needs.
He has more experience of what is best and what is more suitable.
He will be able to purchase it cheaper than you anyway.
Where is this wall, is this an internal wall or is it outside?
Is it 50cm wide (1ft 8in) or do you mean 50mm (2in)?
"Can I run the cable along the edge of this boxed out section"
Do you mean to run it inside the box or outsde?
"is it treated as a new wall"
Dunno can't see it.
Safe...
(1) Correct it must be RCD protected.
(2) As long as it is RCD protected you can use capping; most will still
use plastic capping, as it doesn't have to be earthed.
(3) Steel conduit can be used because it has mechanical protection and therefore doesn't have to be RCD protected. But...
You will no doubt have to have a PIR done on your wiring, which will then highlight the problem and your prospective buyers will undoubtedly demand you put it right before buying the property.
That is assuming it hasn't deteriorated beforehand causing a fire which your insurers won't...
The short answer is no.
You need all the cable replacing, which means renewing the cable from the CU to the first socket if that is the last of the remaining old cable.
I would have thought you would have discussed this with your electrician with a view to him doing it as he is going to be...