It can be “press and open immediately”, as long as it’s possible to choose the brush when releasing the mouse. (Basically how menus work in blender).
Not much, I think. It could be another button. The placement of the button is what matters the most, and top left is kind of the ideal place for that. Also, if the button icon could change based on the active brush, it would be handy.
Oh, I’m sorry, this mockup looks like that because I made it years ago for another topic here, but I posted because the idea still fits.
And no, the 2D icons has no real meaning there.
This popup palette is meant to show a iist of brushes. So if it were made today, it would be filled with the new 3D icons.