So for your first question, a sort of scalloped out cut like that can be done by building a cutting surface using things like loft or sweep and doing the boolean with the surface as the cutting object. That's instead of using just a 2D curve as a cutting object since that will be a straight direction type of cut.
So that looks something like this, here using sweep and boolean difference:
You can adjust the shapes of the sweep profile and rail and also the angle and depth of the surface in relation to the main body to get different looking cuts.
For the base geometry, judging from the patch junctures in these areas I'd say it is likely conversion from a sub-d model for the base shape:
The trick is to click "Face(s)" and not "solid(s)"! (else function don't work)
here "Inward" + "Grooved" on the top face
Union Top and Bottom solids
then Shell the top Face + Fillets on some edges
(with the real time free Simlab Composer lite max 1920 * 1080)
If you want to get some control over cut line position on the helmet, you can project a curve to the side. Since it will be a closed curve, split it in 4 pieces with trim points, so you get 4 sides for network (I highlighted front and back pieces). Add profiles roughly in the middle, they will define depth of the cut, my example is much deeper than on your model.
Narrow cut ("mouth") is obtained again from side projected curve, used as a rail for the sweep.
base_form1.jpg
