Sand at the bottom of the sump as seen in the illustration you posted, will always cause you problems. The way your design is, you have water running through the sand before it reaches the return area. I don't think this will work.
Always rinse out the carbon before adding it. You do not want carbon particles making it to the display. If the skimmer skims more because of this practice, it's simply skimming out carbon particles. Putting carbon in the sump in a bag is not very effective. If you want to run carbon, a better way would be to run it in a reactor. Water must be forced through the carbon for it to be of use.