This is the second part of the work that analyses dynamical energy limits for diverse operations with finite rates important in engineering. Our position is that a dynamic limit of a sufficiently high hierarchy may be helpful in modelling and design of a prescribed operation. In particular, we treat active systems with coupled heat and mass transfer important in separation and biological systems. The operations considered occur in separation units, heat and mass exchangers, energy converters and chemical reactors. The energy limits are expressed in terms of classical exergy and a residual minimum of entropy generated in equipment of a fixed dimension. To ensure physical limits we treat sequential work-driven operations, in particular those of dissolving or evaporation which run jointly with thermal machines (e.g. heat pumps). We also compare structures of optimization criteria describing these limits (in particular "endoreversible limits") in traditional and work-driven operations. Through quantitative analyses we extend to the realm of mass transfer operations the method initiated in Part I that applies "Carnot variables" as suitable controls. Functions of extremum work, which apply a residual minimum entropy production, are found in terms of initial and final states, duration and (in discrete processes) number of stages. Mathematical analogies between entropy production expressions in traditional and work-driven operations are helpful to formulate optimization criteria in both cases.