Let $G \curvearrowright X$ be a free action of a discrete amenable group on a compact metrizable space. For such an action, the properties in the title were defined in the context of classification theory for C$^*$-algebras, and they help answer several important questions about the crossed product. As it turns out, having these properties also allows one to resolve the so-called shift embeddability problem in mean dimension theory. In this talk, we will start by describing the results above and then focus on characterizing the actions that have Uniform Rokhlin Property and comparison.