  We investigate the spin-valley physics (SVP) in MoSe$_2$/WSe$_2$
heterobilayers under external electric field (EF) and changes of the interlayer
distance (ID). We analyze the spin ($S_z$) and orbital ($L_z$) degrees of
freedom, and the symmetry properties of relevant band edges (at K, Q, and
$\Gamma$ points) in high-symmetry stackings at 0 (R-type) and 60 (H-type)
degree angles, the important building blocks of moir\'e or atomically
reconstructed structures. We reveal distinct hybridization signatures of $S_z$
and $L_z$ in low-energy bands due to the wave function mixing between the
layers, which are stacking-dependent and can be further modified by EF and ID.
The H-type stackings favor large changes in the g-factors under EF, e. g. from
$-5$ to $3$ in the valence bands of the H$^h_h$ stacking, due to the opposite
orientation of $S_z$ and $L_z$ in the individual monolayers. For the low-energy
dipolar excitons (DEs), direct and indirect in $k$-space, we quantify the
electric dipole moments and polarizabilities, reflecting the layer
delocalization of the constituent bands. We found that direct DEs carry a
robust valley Zeeman effect nearly independent of the EF but tunable by the ID,
which can be experimentally accessible via applied external pressure. For the
momentum-indirect DEs, our symmetry analysis indicates that phonon-mediated
optical processes can easily take place. For the indirect DEs with conduction
bands at the Q point for H-type stackings, we found marked variations of the
valley Zeeman ($\sim 4$) as a function of the EF that notably stand out from
the other DE species. Stronger signatures of the coupled SVP are favored in
H-type stackings, which can be experimentally investigated in $\sim
60^\text{o}$ samples. Our study provides fundamental insights into the SVP of
van der Waals heterostructures, relevant to understand the valley Zeeman of DEs
and intralayer excitons.
