I decided to discard the square connector and try it in another future part because 2 reasons: 1. I still have to look more on this matter, 2. because I've seen that holes for connectors without pin do not have this square shape, instead have the pin head shape around the holes.
I also solved de North-South schematic pins problem.
This would be the actual PCB:
So this is my new version:
Find the 3rd part in the next post.
Thanks for your time and advice