just a lazy way to describe one displace along normal applied after another, or simply any operation that advects P along any vector until you get to final P and N
in Houdini you can move P around to any position to create displacement, what can be tricky is to compute corresponding N, but however you get to new P doesn't have to be just moving along N or custom vector. Let's say you want to advect P through volume vel in a several steps, well, why not
Mantra still needs to dice geometry to get enough resolution for Displacement or achieve perfect smoothness for Subd, so no, dicing is not only for micropoly, however micropoly has to dice every geo as it's shading corners of micropolygons, in Raytrace mode dicing is purely to generate hi res geo to raytrace against like in mentioned cases
Shading Quality is controlling dicing density based on geometry before displacement
Re-Dicing runs trial dice and displace pass just to measure area of displaced geometry, then adjusts dicing density accordingly and displaces for real, therefore hopefully giving you more micropolys where you need them