Perfection is hard to achieve. Try Daniel tool if it is better for your shape. See there.
It is on purpose. I choose to have common points, so if you want to 3d print a pattern associated with the hexagon it could work. To make it planar is simple.
Extract control point then Planar fit then Project hexagon on plane.
And the fact that hexagon are outside it is also on purpose to keep the topology intact. You can cut after.