1. An exhaustive understanding of the pyramids and secret chambers would be detrimental to the Egyptian mythos. Egypt owns the pyramids. Western Egyptologists need Egyptian cooperation to learn anything new.
2. Sand-filled wind behaves much like an abrasive liquid. There is more sand in the bottom of a sand-filled wind than in the top.
3. Rotation creates surprising perfection, especially when wielded by skilled artisans. It's rarely the tools that bring results.
Abrasive grit. You can make a saw out of a plank with grit -- the grit will eat the plank faster than stone, but it can cut through granite because quartz in the sand is harder than granite. Similarly, you can make a drill with a dowel and grit. The step from drill to lathe is pretty obvious to me.
And don't forget time. People with primitive technology have an astounding amount of patience compared to soft-handed technologists. Speaking as a soft-handed technologist, of course.