Continuing our ongoing investigations of random lasing, we used the Monte Carlo method to simulate random walks of photons within a multiply scattering medium. By initially applying this technique to calculate pulse-stretching in a passive disordered medium, we elucidated its agreement with analytical diffusion theory. Thereafter, we introduced conditions of optical amplification, and reproduced the experimentally observed spectral features like spectral narrowing, intensity enhancement, bichromaticity, mode competition, etc., in a random laser. After investigating diffusive and sub-diffusive regimes of scattering, we formulated our results in terms of a gain subvolume, the functioning of which depends upon local gain conditions. We then used a modified approach of this technique to study ultranarrow random lasing modes, and successfully reproduced these modes observed in a random laser. Based on our simulations, we were able to explain the origins of ultra-narrow lasing modes as excessively amplified extended modes.