Adding a double socket

Hi everyone.

I am trying to add a 1 double socket in a bedroom and just want to ask the right way or be compliant to reg.

1. Are we allowed to DIY adding an additional socket to the current circuit?
2. Are new homes (2018 build) usually radial circuits? I have checked all related sockets on this area and seen one with only 1 set of T&E wire thus it is the end of the circuit and it doesn't feed back to the mcb? Or is there other way to check if its a ring or radial?
3. if it is radial, is it fine to add a spur from an existing socket granted to use the same wiring size (eg. 2.5mm on 20A breaker)
4. In terms of running the spur wire from an existing socket, which way is acceptable.

• Horizontally - this is the easiest way as would only need 2.5m of wire and I can run it through the small gap between the stud and concrete wall (dont think its the external wall as looking from the attic its drywall - stud (2x2) - 1.5-2cm gap (where I plan to run the wire) - concrete - gap/insulation? - brick wall (external)). But my concern on this is it will run behind where the radiator of the room is mounted. will this be a concern even if the wire don't have a direct contact with the internal drywall as it is separated by the 2x2 stud?
• Vertically - I can run the wire vertically from existing socket then across the attic then down to the new planned socket, but this will take around 7.5-8m of wire length also not sure if I would need to notch or make a hole in the top plate of the wall or if there is space I could slip the wire through.

Diagram below for reference of my scenario:

thanks