Oh god, that was it. It's me using my smartphone, instead of the PC. When you open the tilemap tab, the layout is not on the screen, so I never though it that way- clicking in the tab, then onto the layout. I am starting to work on PC for preventing this sort of misunderstanding.
Moreover, I didn't quite understand the purpose of the tileset at all. Now I do. You load every different tile grouped in the tileset and then pick which tiles go where. I am no native english speaker, so some words don't ring my bell as they should. Being tileset what you edit in the tab, not tilemap, now it seems so obvious.
Sorry for the loss of time, but again thanks a lot for you have gave me some hints of how to work around it. Lots of tutorials to read, now that I can move on.
Not sure if I am asking nonsense again but- tiled background loops the same sprite. Tilemap lets you assign certain sprites (tiles actually, but for the sake of analogy). Is there a way of loading a picture, as per the tileset, and move every tile to the layout in the same order they are in the loaded picture? It would be the same as when you set up the grid onto the layout in the properties bar. But locking that grid to make it visible in prev and game. If you take a look at my map, there are to be several tiles and I want the layout to look exactly like my map, just with a grid.