How can I measure the scale in water?
Most drinking water has residue like what you are showing.  Boiling water shows there are ions in the water, but it does not show what kind of ions are present.  Boiling water is practically useless when determining scaling potential and it is not safe to do using cooking pots and pans.  Part of the reason laboratory equipment is more expensive than cooking pots and pans is because lab equipment has much better fire prevention measures.  Boiling down water in this manner has the potential to start a fire.
pH is a better measure for scaling potential.  If you want to get technical, water pH is used to determine the Langelier Saturation Index or the Ryzner Index which are indicators of scaling potential.
Your water is probably too alkaline. Alkalinity and acidity need to be balanced because if water is too alkaline then too much scale forms; however, if the water is too acid pipes corrode.
For a household, filtering water with an activated carbon filter first, then an ion exchange filter might work.  Ion exchange filters contain a resin which exchange scale forming ions like calcium with ions like sodium. These filters can be easily fouled by organic material, so the organic material will need to be removed by something like an activated carbon filter.