  Thermal dust polarization is a powerful tool to probe magnetic fields
($\textbf{B}$) and grain properties. However, a systematic study of the
dependence of dust polarization on grain properties in protostellar
environments is not yet available. In this paper, we post-process a non-ideal
MHD simulation of a collapsing protostellar core with our updated POLARIS code
to study in detail the effects of iron inclusions and grain growth on thermal
dust polarization. We found that superparamagnetic (SPM) grains can produce
high polarization degree of $p \sim 10-40\%$ beyond $\sim 500$ au from the
protostar because of their efficient alignment by magnetically enhanced
Radiative Torque mechanism. The magnetic field tangling by turbulence in the
envelope causes the decrease in $p$ with increasing emission intensity $I$ as
$p\propto I^{\alpha}$ with the slope $\alpha \sim -0.3$. But within 500 au, SPM
grains tend to have inefficient internal alignment (IA) and be aligned with
$\textbf{B}$ by RATs only, producing lower $p \sim 1\%$ and a steeper slope of
$\alpha \sim -0.6$. For paramagnetic (PM) grains, the alignment loss of grains
above $1\mu m$ in the inner $\sim 200$ au produces $p << 1\%$ and the
polarization hole with $\alpha \sim -0.9$. Grain growth can increase $p$ in the
envelope for SPM grains, but cause stronger depolarization for SPM grains in
the inner $\sim 500$ au and for PM grains in the entire protostellar core.
Finally, we found the increase of polarization angle dispersion function $S$
with iron inclusions and grain growth, implying the dependence of B-field
strength measured using the DCF technique on grain alignment and grain
properties.
