Hey Matthieu, yep, heaps of ideas!!! Firstly, well done for recognising the inconsistencies in your sound – Critical awareness of the problem is half the solution!
Clearly you are using too much muscle strain to get the higher notes out – DON’T PANIC – you are not alone and that is fine at the start. What part of YOUR range feels like humming/singing? As you will have learned going through the Singing C exercises, playing above the stave efficiently is very complicated.
When coming down to the lower notes, you are not yet sure of the SHAPE required AND you have pinched the lip tissue when playing the higher notes and then keeping it pinched.
Refine your awareness of each note and learn to change between notes without over-exerting.
Stick with it!