wow ! I didn't expect such an expert answer. you actually got me completely lost. ahahah. (I'm nearly a beginner !).
I'm planning to re-do the circuit from scratch. Maybe I did something wrong.
If after this, it goes wrong again, I'll go through your complete troubleshooting process.
fyi, I've got a multimeter (fluke 189) but no oscilloscope (if you have advise on cheap/diy oscilo/DSO, I'll hear them ;)).
... I'll post the conclusions here (don't hold your breath, I really have little time for personnal hobbies those days).
Anyway thanks tons for your answer.