The effects of impurities on runaway electron generation are studied using a zero-dimensional disruption simulation code. For describing collisions between fast electrons and partially stripped ions, a charge-resolved expression of the Coulomb logarithm is employed. Numerical analysis of the avalanche growth rate using the adjoint Fokker-Planck method is compared with two existing semi-analytic models, showing (i) the convergence of the growth rate to strong electric field limit of the Rosenbluth-Putvinski (R-P) model and (ii) the cancellation of the effect of second-order collisional diffusion for intermediate electric fields. Using the developed current quench (CQ) simulations, the parametric study is performed with the aid of the power balance analysis, whichcharacterizes the onset of strong avalanche amplification in the presence of low-Z and noble gas species. Thermal quench (TQ) simulations are also developed for self-consistent evaluation of hot-tail seed electrons. The deposition timescale of impurity neutrals is shown to have significant impacts on hot-tail seeds, depending nonmonotonically on the pre-TQ temperature and the injected impurity density.