In Paper I [Garrigues et al., Phys. Plasmas 31, 073907 (2024)], we have extended the sparse PIC approach already used in the literature with the offset scheme to reduce the grid-based error. In this study, we demonstrate the ability of the offset sparse PIC algorithm to model partially magnetized low-temperature plasmas by reducing the grid-based error. In the context of multi-cusp magnetic field configurations, the offset scheme reduces the error of the current collected at the walls to less than 5% for more of the plasma conditions encountered in ion source applications. The formation of a double layer in the sheath region is also captured. In the context of the electron drift instability that occurs in the Hall thruster, the plasma properties as well as the ion velocity distribution function can be retrieved with a high enough precision without considering an initial regular grid with a smaller mesh resolution. The results also highlight the advantage of combining the electric potential at the nodes of the regular grid instead of directly combining the electric field from the component grids. Compared to the regular PIC algorithm, the typical speed-up factor is about three for a number of mesh nodes of 256$^2$ and five for 512$^2$