Silly Question
 

When you're measuring your waist, do you measure where your waist is the smallest, or just above your belly button, or at your belly button? Because obviously where my waist is smallest isn't where I wear my pants... or where I carry most of my abdominal weight. May sound silly, but I'd really like to know - thanks!

For my own benefit, I measure at the smallest part. For some body composition calculators the instructions tell you where to measure, like at the umbilicus.
If you are keeping records for your own historical calculations, just make sure to always measure in the same place.

Does anyone know where to measure the waist to calculate waist/hip ratio?

I believe for waist/hip it's at the smallest part. I always specify when I answer such as right now there's a thread on the support forum asking measurements so I gave both.

most people go by the "natural waist" which would be the smallest diameter. The hip is usually measured where the largest diameter is (right between the pelvis and thighs, for most people?)

Yup, if you're going for the waist/hip ratio you measure the smallest part of your waist and the largest part of your hips. Same for when you're figuring your your proportions, but unfortunately clothes don't have the same opinion as nature as to where your waist is. I like how on OldNavy.com it actually shows you where to measure for pant sizes!