Dust properties and star formation of approximately a thousand local
  galaxies
  [ABRIDGED] We derive the dust properties for 753 local galaxies and examine
how these relate to some of their physical properties. We model their global
dust-SEDs, treated statistically as an ensemble within a hierarchical Bayesian
dust-SED modeling approach. The model-derived properties are the dust masses
(Mdust), the average interstellar radiation field intensities (Uav), the mass
fraction of very small dust grains ('QPAH' fraction), as well as their standard
deviations. In addition, we use mid-IR observations to derive SFR and Mstar,
quantities independent of the modeling. We derive distribution functions of the
properties for the galaxy ensemble and per galaxy type. The mean value of Mdust
for the ETGs is lower than that for the LTGs and IRs, despite ETGs and LTGs
having Mstar spanning across the whole range observed. The Uav and 'QPAH'
fraction show no difference among different galaxy types. When fixing Uav to
the Galactic value, the derived 'QPAH' fraction varies across the Galactic
value (0.071). The sSFR increases with galaxy type, while this is not the case
for the dust-sSFR (=SFR/Mdust), showing an almost constant SFE per galaxy type.
The galaxy sample is characterised by a tight relation between Mdust and Mstar
for the LTGs and Irs, while ETGs scatter around this relation and tend towards
smaller Mdust. While the relation indicates that Mdust may fundamentally be
linked to Mstar, metallicity and Uav are the second parameter driving the
scatter, which we investigate in a forthcoming work. We use the extended KS law
to estimate Mgas and the GDR. The Mgas derived from the extended KS law is on
average ~20% higher than that derived from the KS law, and a large standard
deviation indicates the importance of the average SF present to regulate star
formation and gas supply. The average GDR for the LTGs and IRs is 370, while
including the ETGs gives an average of 550. [ABRIDGED]
