The "Sand Texture": Don't panic if the dough looks crumbly in the bowl (like wet sand). As long as it clumps together when squeezed, it is perfect. If you overmix it to try and make it a solid ball, the cookies will be tough.
Why the Double Chill? Chilling the dough flat makes it easier to cut clean shapes without sticking. Chilling the cut shapes solidifies the butter so they don't puddle in the oven.
Re-rolling Scraps: You can gather the scraps and re-roll them, but they may need to be chilled again if the dough gets too warm/soft to handle.