  The formation of the first galaxies during cosmic dawn and reionization (at
redshifts $z=5-30$), triggered the last major phase transition of our universe,
as hydrogen evolved from cold and neutral to hot and ionized. The 21-cm line of
neutral hydrogen will soon allow us to map these cosmic milestones and study
the galaxies that drove them. To aid in interpreting these observations, we
upgrade the publicly available code {\tt 21cmFAST}. We introduce a new,
flexible parametrization of the additive feedback from: an inhomogeneous,
$H_2$-dissociating (Lyman-Werner; LW) background; and dark matter -- baryon
relative velocities; which recovers results from recent, small-scale
hydrodynamical simulations with both effects. We perform a large, "best-guess"
simulation as the 2021 installment of the Evolution of 21-cm Structure (EOS)
project. This improves the previous release with a galaxy model that reproduces
the observed UV luminosity functions (UVLFs), and by including a population of
molecular-cooling galaxies. The resulting 21-cm global signal and power
spectrum are significantly weaker, primarily due to a more rapid evolution of
the star-formation rate density required to match the UVLFs. Nevertheless, we
forecast high signal-to-noise detections for both HERA and the SKA. We
demonstrate how the stellar-to-halo mass relation of the unseen, first galaxies
can be inferred from the 21-cm evolution. Finally, we show that the spatial
modulation of X-ray heating due to relative velocities provides a unique
acoustic signature that is detectable at $z \approx 10-15$ in our fiducial
model. Ours are the first public simulations with joint inhomogeneous LW and
relative-velocity feedback across the entire cosmic dawn and reionization.
