We report on theoretical and experimental investigations of gain dynamics in Raman fiber lasers in the frequency range of 1 Hz-1 MHz. An analytical solution of the problem is due to the nonlinear nature of the Raman effect not feasible. Thus, we used a numerical simulation to gain general insights. Experimentally and numerically obtained results for a Raman fiber laser emitting at 1180 nm show good qualitative agreement. We also present a potential physical interpretation of the observed dynamical properties. In addition, we report on an experimental proof-of-principle of a passive pump-to-Stokes RIN suppression scheme for the main Stokes order in cascaded Raman fiber lasers utilizing an additional parasitic Stokes order. Again, results from numerical and experimental studies of a cascaded Raman fiber laser at 1180 nm and 1240 nm show good agreement and confirm the passive pump-to-Stokes RIN suppression at 1180 nm. The dependencies between the resonator design and the parameters of the noise suppression are investigated. In addition, it is shown that the scheme can also be applied to cascaded Raman fiber lasers with more then two Stokes shifts. This opens the possibility to design for example low-noise Raman fiber lasers at 1480 nm to pump low-noise Er(3+) doped fiber amplifiers.