„Naught conductor“ sounds like a good old dictionary translation of the German „Nullleiter“. The official term these days is „Neutrallleiter“ but most people still use the older term.
The one thing I do find interesting is that all European countries I‘m aware of have a minimum requirement of 1.5 mm2 for
mechanical strength in fixed installations (except control circuits). The UK and Ireland are the only exceptions as far as I know.
Is the current circuit on an RCD with other circuits or on its own RCBO? If the latter and it only serves laundry appliances I‘d say spurring off this circuit is fine, otherwise I‘d recommend adding an extra RCBO as JohnD suggested.
In my opinion the difference does matter, an ES27 lamp in an ES26 socket will leave much more screw thread exposed than it should. Yes, that should be connected to the neutral but you aren‘t supposed to have permanently bare neutrals either.
French homes these days are required to have DCL...
Many countries using CEE 7 plugs require sockets to be protected at no more than 16 A and all extension leads to be rated at 16 A, so no amount of creative splitting could cause an overload beyond the trip curve of the MCB. There is one exception, power strips with no more than four CEE 7/16...
Spring-loaded terminals have been around since the 1970s and quite a few countries on the continent have been using them almost exclusively for the better part of 30 years (German manufacturers pretty much abandoned sockets with screw terminals when the VDE allowed spring-loaded terminals in...
The downstairs switch has to be wired incorrectly, it only has two wires connected, any 2-way setup would need three. Considering how bad the newer wiring looks I wouldn‘t feel confident going wireless without fixing that lash-up. Time to lift some floor boards I‘m afraid.
I happen to live in a country where over-sleeving isn‘t allowed either (at least for earth, neutral is a bit of a grey area) and the answer to the fan question is „use five core“ (full-sized, insulated earth, so it counts as a full core).
The main question was whether that was just a plug (seems most likely now) or a small-ish power supply. If it happened to be the latter, fitting a mains plug to the cable would result in a fairly spectacular meltdown. Electronics designed for something like 5 or 12 V DC don't take kindly to...