This thread has missed several of your questions. Yes, you should be fusing any mains connections into a device you are controlling. Sizing will depend upon the loads and the relays selected for which you have provided no information.
This comment:
I have also thought of cutting cable extenders (1 cable from each line) to put them in the relay, but I would like to know if I should put a fuse in each and how they should be separated according to a norm.
Makes no sense whatsoever to me. Could you please explain what you mean by cutting a cable from each one?
As a general comment, the majority of the Chinese 1/2/4/8/16 channel relay boards sold as Arduino compatible devices would not pass a CE hazard assessment if used in a commercial product due to the clearance and creepage distances in the pc board layouts. The actual physical relays are okay (in most cases) but the board designs are usually lacking the required spacing. Most boards also lack the extra cost step of creating an air gap between the high voltage contact side of the relays.
The are other factors that must be considered as well, the most important being proper earthing when connecting to mains voltages. As mentioned, it would best to consult a qualified electrician in your country if you are unfamiliar with the necessary methods to realize a safe and reliable installation.