We comprehensively study nonequilibrium relaxation and aging processes in the two-dimensional randomsite Ising model through numerical simulations. We discuss the dynamical correlation length as well as scaling functions of various two-time quantities as a function of temperature and of the degree of dilution. For already modest values of the dynamical correlation length L deviations from a simple algebraic growth, L(t)similar to t(1/z), are observed. When taking this nonalgebraic growth properly into account, a simple aging behavior of the auto-correlation function is found. This is in stark contrast to earlier studies where, based on the assumption of algebraic growth, a superaging scenario was postulated for the autocorrelation function in disordered ferromagnets. We also study the scaling behavior of the space-time correlation as well as of the time integrated linear response and find again agreement with simple aging. Finally, we briefly discuss the possibility of superuniversality in the scaling properties of space- and time-dependent quantities.