I would like to put this pattern on the non spherical face but when I project it creates a radial pattern that I don't want. I tried to use the wrap function but it doesn't work on on planar faces? How can I project then cut with this pattern onto the surface?
I approached this first with surfaces, creating a circular pattern of 100 (guessed, adjust as you need) extrude surfaces based on the conversion onto the Front plane of one of your sketch entities.
This didn't work, as SolidWorks seems to go in an endless loop with the 100 surfaces. I then made 100 copies of a solid extrusion, trimmed it with a surface offset 0.3mm inside the original outside surface, and finally did a subtract of all that.
The problem is greatly complicated by the fact that your part is not a revolution. You might have a good reason for that so this solution works on the non-round part.
I hope this helps.