Why so many grays?

I looked at your part. Some of the “grey” you might be seeing is sketchup altering the shading of surfaces as you move/orbit around your model to help the object appear more 3D. This is useful usually but if you want to you can check “use sun for shading” in the Shadows window to adopt one perspective lighting that will not change as you move.

The darker grays you see that are not shifting as you move around indicate faces that are reversed. The back side of the face is facing outward and needs to be corrected. You can accomplish this by selecting the face and right clicking, then select reverse face.