2) Clicking on the buttons causes a redraw, and that may lead to the Fl_Group is "blinking". Is the problem that my Fl_Gl_Window/draw() uses too much time ?

Redrawing a UI within a GL window is different to a regular window. A GL window must always be redrawn in its entirety (*including* the 3D scene in the background), whereas system windows use clipping and other tricks to redraw only what's needed. Again, I'll be happy to look into that, but I will need more detail, and probably some sample source code that shows the unexpected behaviour. The overridden Fl_Gl_Window::draw() function should redraw the entire 3D scene first, and then call the original draw() function.