a) can we add new fields in the Treatment group and only for projects ?

Yes, you can add new fields on any screen

b) can we force the user to update specific fields on state transition ?

Yes, you can set field as required depending on status

c) can we automatically clear specific fields on state transition ?

No

]d) can we automatically update a new date field (with the current date) on state transition ?

No, only default value can be defined, set on creation

For each point, is it configurable or do I need to code ?

All is defined through Screen customization form.
No coding at all.

I have many many administrative new fields to add in the project view.

I want to integrate them in a way that do you overload the view.

So i wanted to add them, like a block of attributes that can be hide (throught a clic).

I check your design, and it seems that you have a table (1-1 relationship with an unique project) for each group of attributes.

is it possible to declare a new table with those attibutes ? and then display them likes them like descrition, progress, treatments groups ..

Or do have another way to handle such request ?

Thx

You can easily do this with "screen customization" plugin.
You just add a section that will contrain new fields.