A recently developed method to calculate the neoclassical viscosity, diffusion, and current coefficients in general nonsymmetric toroidal plasmas by using the direct solution of the linearized drift kinetic equation with the pitch-angle-scattering collision operator is applied to impurity transport problems and bootstrap current calculations in stellarators. In this new method based on the basic idea of the so-called moment approach, the collisional momentum conservation is taken into account, and thus, it is applicable to the heat and particle diffusivity in advanced stellarators with quasi symmetry, and also to plasma flows currents, and viscosities in general nonsymmetric multispecies plasmas. In this paper, the impurity flow and the bootstrap current observed in the neoclassical internal transport barrier operation in the Compact Helical System are compared with theoretical calculations. Another topic is the benchmark test of existing analytical expressions for the bootstrap currents by comparing with numerically obtained current coefficients. The geometric factor, which is required for the current calculation based on the moment method, given by our new method is compared with these formulas.