Hopefully this will help you hit your target.
Offset a plane and make it half the diameter of your part or larger (ctrl+drag a plane to start, then type in the distance). Pic 1
Pick the new plane, then sketch your door and offset that rectangle. Cut-extrude it, and pick the "Offset from surface" option. If the cut doesn't work the first time, hit the flip arrow next to the Offset from surface selection. Pic 2.
You should now have the cutout of the door, and the border around the door. Pic 3.
Pick the offset plane again, and draw the circle for the cut-out, and the slot and half-circles for the screw heads. Pic 4.
Pic 5 is the final outcome, your mileage may vary.