Well, first thing first : I think I'm stupid.
Using a FixedSize UIRoot allows me to avoid all my UIStrech call, and to set the sizes I want in my "original template", with a nice an smooth resize.
Second thing : this should NOT be in the last tutorial of the serie. Multiplatform developpers will be gratefull

I still have some positionning problems, but I guess I will be able to fix them with the same method.
I still would like to use relative (% size of parents) values for the anchors though.
Edit : Well, the problem is that the anchor values do not scale like the rest (size values for example). Plus, the relative anchor size is definitely doing weird things. I will try to explain my problem in a clearer way.
Here is what I want :
- Cutting the background depending of the resolution and resize it correctly. I managed this using a UI2DSprite with UIStrech script attached which force the picture to respect its original ratio :

- Now I would like to position my two buttons like this :

The problem is that the anchor size between my 2 buttons seems fixed : I'm not sure it is resizing considering the UIRoot FixedSize property. It seems to be resizing correctly ! Yeah!
And the relative anchors are not working so well (or I don't use them correctly), as you can see here:

I was trying to use a 0.73 relative anchor on my left button. But using "0" did not move my button. Is it just an UI problem, or something that I don't quite get correctly ?
tl:dr : Seems that my anchor value between my 2 buttons is working correctly (the distance seems to scale nicely). But the problem with my "fixed" anchor on the left button (to fix its x position) is that when the ratio is changing (4/3 >> 16/9) it does not work correctly. I have to use a percentage here.