We present new low-resolution (R~800) optical spectra of 22 Galactic PNe with Spitzer spectra. These data are combined with recent optical spectroscopic data
available in the literature to contstruct representative samples of compact (and
presumably young) Galactic disc and bulge PNe with Spitzer spectra. Attending to
the nature of the dust features - C-rich, O-rich and both C- and O-rich dust
features (or double chemistry) - seen in their Spitzer spectra, Galactic disc
and bulge PNe are classified according to four major dust types (oxygen
chemistry or OC, carbon chemistry or CC, double chemistry or DC, featureless or
F) and subtypes (amorphous and crystalline, and aliphatic and aromatic) and
their Galactic distributions are presented. Nebular gas abundances of He, N, O,
Ne, S, Cl and Ar, as well as plasma parameters (e.g. Ne, Te) are homogeneously
derived by using the classical empirical method. We study the median chemical
abundances and nebular properties in Galactic disc and bulge PNe depending on
their Spitzer dust types and subtypes. Differences/similarities between PNe in
the Galactic disc and bulge are reported. In particular, the median abundances
for the major Spitzer dust types CC and OC are representative of the dominant
dust subtype (which are different in both Galactic environments) while these
values in DC PNe are representative of the two DC subtypes. A comparison of the
derived median abundance patterns with AGB nucleosynthesis predictions show
mainly that: i) DC PNe, both with amorphous and crystalline silicates, display
high-metallicity (solar/supra-solar) and the highest He abundances and N/O
abundance ratios, suggesting relatively massive (~3-5 M_sun) hot bottom burning
AGB stars as progenitors; ii) PNe with O-rich and C-rich unevolved dust
(amorphous and aliphatic) seem to evolve from sub-solar metallicity (z~0.008)
and lower mass (<3 M_sun) AGB stars; iii) a few O-rich PNe and a significant
fraction of C-rich PNe with more evolved dust (crystalline and aromatic,
respectively) display chemical abundances similar to DC PNe, suggesting that
they are related objects. A comparison of the derived nebular properties with
predictions from models combining the theoretical central star evolution with a
simple nebular model is also presented. Finally, a possible link between the
Spitzer dust properties, chemical abundances and evolutionary status is
discussed.