Recovering galaxy stellar population properties from broad-band spectral energy distribution fitting

(Abridged) We explore the dependence of galaxy stellar population properties derived from broad-band SED-fitting - such as age, stellar mass, dust reddening, etc. - on a variety of parameters, such as SFHs, metallicity, IMF, dust reddening and reddening law, and wavelength coverage. Mock galaxies serve as test particles. We confirm our earlier results based on real z=2 galaxies, that usually adopted \tau-models lead to overestimate the SFR and to underestimate the stellar mass. Here, we show that - for star-forming galaxies - ages, masses and reddening, can be well determined simultaneously only when the correct SFH is identified. This is the case for inverted-\tau-models at high-z, for which we find that the mass recovery (at fixed IMF) is as good as ~0.04 dex. Since the right SFH is usually unknown we quantify offsets generated by adopting standard fitting setups. Stellar masses are generally underestimated resulting from underestimating ages. For fitting setups with a variety of SFHs the median mass recovery at z ~ 2-3 is as decent as ~0.1 dex, albeit with large scatter. The situation worsens towards lower redshifts because of the variety of possible SFHs and ages (~0.6 dex at z=0.5). A practical trick to improve upon this is to exclude reddening from the fitting to avoid unrealistically young and dusty solutions. Reddening and SFRs should then be determined by a separate fit. As expected, the recovery of properties is better for passive galaxies. For the two galaxy types the parameter recovery is optimal for a wavelength coverage from the rest-frame UV to the rest-frame near-IR. We quantify the effect of narrowing the wavelength coverage or adding/removing filters which can be useful for planning observational surveys. Finally, we provide scaling relations that allow the transformation of stellar masses obtained using different template fitting setups and stellar population models.