  Using the dcQMD transport model, the isoscalar and isovector in-medium
potentials of the $\Delta$(1232) baryon are studied and information regarding
their effective strength is obtained from a comparison to experimental pion
production data in heavy-ion collisions below 800 MeV/nucleon impact energy.
The best description is achieved for an isoscalar potential moderately more
attractive than the nucleon optical potential and a rather small isoscalar
relative effective mass m$^*_\Delta \approx$ 0.45. For the isovector component
only a constraint between the potential's strength at saturation and the
isovector effective mass difference can be extracted, which depends on
quantities such as the slope of the symmetry energy and the neutron-proton
effective mass difference. These results are incompatible with the usual
assumption, in transport models, that the $\Delta$(1232) and nucleon potentials
are equal. The density dependence of symmetry energy can be studied using the
high transverse momentum tail of pion multiplicity ratio spectra. Results are
however correlated with the value of neutron-proton effective mass difference.
This region of spectra is shown to be affected by uncertain model ingredients
such as the pion potential or in-medium correction to inelastic scattering
cross-sections at levels smaller than 10$\%$. Extraction of precise constraints
for the density dependence of symmetry energy above saturation will require
experimental data for pion production in heavy-ion collisions below 800
MeV/nucleon impact energy and experimental values for the high transverse
momentum tail of pion multiplicity ratio spectra accurate to better than 5$\%$.
