Drainage is the main reason to raise beds so I would put the bed atop the sand mix.

Yeah, I don't think I would till sand and rock into the soil. If you're growing relatively small plants, not big shrubs and trees with deep roots, 16" might be enough.

The worst thing that could happen is that it drains TOO well because of the sandy stuff underneath. I don't know what kind of native soil you have. If it's heavy clay underneath, the sand/gravel could fill with water during wet weather and it would just kinda sit under there. Might not be a bad thing in hot dry weather. But if your soil is very sandy anyway, it would probably drain even faster.