A number of modern technological applications require a detailed calculation of the physical properties of aggregated aerosol particles. For example, in probing soot aerosols by the method called laser-induced incandescence (LII), the soot clusters are suddenly heated by a short, powerful laser pulse and then cool down to the temperature of the carrier gas. LII sizing is based on rigorous calculation of the soot aggregate heat-up and cooling and involves prediction of laser light absorption and energy and mass transfer between aggregated particles and the ambient gas. This paper describes results of numerical simulations of the mass or energy transfer between the gas and fractal-like aggregates of N spherical particles in either the free-molecular or continuum regime, as well as the light scattering properties of random fractal-like aggregates, based on Rayleigh-Debye-Gans (RDG) theory. The aggregate geometries are generated numerically using specially developed algorithms allowing "tuning" of the fractal dimension and prefactor values. Our results are presented in the form of easily applicable scaling laws, with special attention paid to relations between the aggregate gyration radius and the effective radius describing various transport processes between the aggregates and the carrier gas.