When i try to add a vertex with Ctrl+R and scale down, that happens:
What can I do so these vertex join all edges?
It appears to be a duplicate vertices/faces issue. Basically, there are two (or more) vertices where there should be one, creating unwanted geometry.
This is the problem:
The simplest solution is to select all of the vertices and to use the Remove Doubles option to automatically remove the overlapping geometry as show below: