Thanks a lot to both of you. This way of doing the menu is brilliant. I just had to change pageRef = ... to url = ... to make it work (thanks to this page in the docs).
For the {{ .Section }}, the problem is that the homepage/index is not considered a section. Therefore, {{ .Section }}is empty on the homepage. Furthermore, when in a section, this syntax does not allow to use the title given in section1/_index.md or section2/_index.md.
P.-S. : @jmooring you helped me the other day on this topic, and just so you know, I made the FAQ as you advised. I am now very happy with this solution.