  We present a DFT-based investigation of the twist-angle dependent proximity
spin-orbit coupling (SOC) in graphene/TMDC structures. We find that for
Mo-based TMDCs the proximity valley-Zeeman SOC exhibits a maximum at around
15--20{\deg}, and vanishes at 30{\deg}, while for W-based TMDCs we find an
almost linear decrease of proximity valley-Zeeman SOC when twisting from
0{\deg} to 30{\deg}. The induced Rashba SOC is rather insensitive to twisting,
while acquiring a nonzero Rashba phase angle, $\varphi \in [-20;40]${\deg}, for
twist angles different from 0{\deg} and 30{\deg}. This finding contradicts
earlier tight-binding predictions that the Rashba angle can be 90{\deg} in the
studied systems. In addition, we study the influence of several tunability
knobs on the proximity SOC for selected twist angles. By applying a transverse
electric field in the limits of $\pm 2$ V/nm, mainly the Rashba SOC can be
tuned by about 50\%. The interlayer distance provides a giant tunability, since
the proximity SOC can be increased by a factor of 2--3, when reducing the
distance by about 10\%. Encapsulating graphene between two TMDCs, both twist
angles are important to control the interference of the individual proximity
SOCs, allowing to precisely tailor the valley-Zeeman SOC in graphene, while the
Rashba SOC becomes suppressed. Finally, based on our effective Hamiltonians
with fitted parameters, we calculate experimentally measurable quantities such
as spin lifetime anisotropy and charge-to-spin conversion efficiencies. The
spin lifetime anisotropy can become giant, up to $10^4$, in encapsulated
structures. The charge-to-spin conversion, which is due to spin-Hall and
Rashba-Edelstein effects, can lead to twist-tunable non-equilibrium
spin-density polarizations that are perpendicular and parallel to the applied
charge current.
