Sorry for not giving news for the past days. I have been very busy trying out to restore a fully operational user session. While I was trying it blew all my menus and I was having a hard time.
As my contribution, here is a summary of what I did.
I understood that when it deals with 2D (whether unity session or gnome-classic session ), it is handled through metacity) whereas when it comes to 3D it is compiz. I realized that the problem came from compiz, and i remembered that I had changed one parameter in ccsm, which resulted in a question "some plugins may be uncompatible, do you want to go on" (the idea, not the exact words !). As a lesson to other users: DON'T ANSWER YES IF YOU ARE RUNNING GNOME CLASSIC. It ruins the environment. Despite all my efforts, I was not able to restore it. From a user standpoint, everything acts as if there were conflicts between options used by compiz in the 2 environments.
From all the posts I read, the best I found that gave me hints to solve the problem was:
I followed the tips but none of them gave me the solution.
I did not switched to GDM because it did not seem to me it would solve the problem. What I did instead what to rely on the observation I made in my first post:
I created a new user from scratch and copied patiently from one user to the user, trying not to copy what seemed to be in connection with compiz.
I then created another user and I can log in normally for this user, but it is impossible to do it for my main user.
After five days of hard labour, it works now.: 3D and everything restored
There may be much simpler solutions, but I failed to find them.
Thank you both for your help.