I'm sorry Paul, I think you lost me there 
I have a bit of electrical knowledge, but very basic, and I got a bit confused with the above explanation (which I appreciate nonetheless). I guess it really doesn't matter anymore, as I finally decided to switch back to the individual relay modules that are high level trigger.
This is currently working fine, but it's a bit unstable, sometimes doesn't seem to be working as it should, but I think it's actually related to either a wire not making a proper connection or faulty relays rather than a circuit design.
When you say they must run separatedly from that point to each part, are you actually telling me that the below two schematics are not the same? After all, all grounds and all 5V are connected together both ways.
I have to build another "module" for another part of the house. This other module will have to manage 2 lights and 2 shutters, so I've purchased a 6 channel module this time. Since these compact PSU are not very expensive, I'm going to use two of them, to have separate PSUs for the ESP and for the relay module. Hopefully that'll make it more stable. This is how I plan to wire it up, in case you spot something wrong about it:
The orange rectangle will be a set of 2.54 pins that I'll use to connect the relay module.
One last question. It is tipically said that a standard value for a pull-down resistor (for the low value of a switch, for instance) is 10K. Can I use 5K instead? or higher? I ran our of 10K resistors, but I have plenty of other values.