  (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.
