I’m almost giving up because I lost 4 hours of modelling and experimenting, and always I end up with a mess of polys :’(
Then I tried to use the same tools on a simple Cube. The Shift-K, without selecting a poly, cuts through the cube like butter; I press TAB and all looks fine.
But, when I apply the same tool with a single poly (because on some places I need more points to give roundness and to separate volumes), I press TAB and everything is good but that poly where I applied the cut :’(
It happens even when I use Subdivide, Split and such. The polys don’t merge good with the rest of their neighbourghs, and that destroys much of my practice works… Sorry, I’m very sad, because I’m a novice and I recent started with 3D and then I crash against this impediment, wich frustrates a lot my creativity and wishes of carry on with 3D 
The picture of sample:

I hope someone can point me what I’m doing wrong, because I watched lots of tutorials using the Cut tool, and really I need it for making extra points and edges on precise places.
I felt comfy making triangles to try to fix the gaps while modelling in unsubpatch mode. Fortunatelly, gaps aren’t now that common as I learn to model properly without using the Knife tool and such.
