LAN and Wi-Fi "devices" per floor?

What you write is completely correct. The setup is [Router in the basement] --(one cable)-- [Switch in the basement]--(many cables)--[Patch panel in the basement]--(many cables)--[Room connection]. "Actually," you could also omit the patch panel; it does nothing. But it allows you to firmly screw down the cables from the rooms and then connect the respective patch panel port to the switch. The switch, in turn, brings the data from the many rooms onto the one cable to the router. Even a simple TP-Link TL-WR940N WiFi router for €20 does everything you want in the room. The data rate is also completely sufficient. The only reason for "faster" WiFi might possibly be simultaneous transmission via multiple WiFi devices (six kids streaming Netflix on their phones). Then it is good to go a bit more expensive, e.g. Linksys EA7500v3 for €50. All these inexpensive access points / WiFi routers work with their own power supply, i.e. you need a power outlet for them and the cable lies around. In contrast, with PoE the power comes via the LAN cable and you can save the power outlet. The devices are a bit more expensive, e.g. NETGEAR WAX214 for €100 and usually have NO additional LAN port, i.e. LAN (from your router/switch/patch panel) goes in, but there is no port for a PC or TV. So suggestion: where multiple devices really should be connected via cable (e.g. living room) place a router WITHOUT PoE, then you have multiple ports and plenty of power. In the other rooms place a WiFi access point WITH PoE, then the ugly cable to the power outlet is omitted.

The discussion can now be carried on endlessly. The devices that probably make sense here are usually sold as "Wi-Fi routers"...

He only needs one router in the network.

With 14 connections, I wouldn’t take a 16 port switch but go straight for a 24 port switch. I also wouldn’t get the device from the electrician but organize it myself afterwards. Passive technology by the electrician, active technology done by myself.

Duplex cables are nothing other than two single network cables "glued together." I would let the electrician decide which of the two to use. Always install each network socket as a double socket and in places where possibly more devices may be needed (office, TV, ...) also more than one double socket. Then there’s the topic of access points for WLAN. Personally, I would only put them on the ceiling and operate them via POE. Of course, a cable has to go there and a small socket behind the access point to hide everything. If the ceiling is not possible for some reason, then up high on the wall. The position of the access points depends on the floor plan and user behavior. Without information regarding that, nothing can be said except that usually at least one access point per floor is installed. Usually, network planning only considers the living space, but one should not forget the rest either. Outdoor access points, network in the garage (wallbox), network for inverters, network for the door intercom, cameras, ... Here we are back to POE and if you have many devices, you use a POE switch. So you see that you can only say what kind of switch you want or need with the existing components.

Recommendation for a product for access point wall mounting

It should probably say: "he only needs one router in the network".

The mentioned TP-Link router is totally outdated and very slow.