  The first bright objects to form in the Universe might not have been
"ordinary" fusion-powered stars, but "Dark Stars" (DSs) powered by the
annihilation of dark matter (DM) in the form of Weakly Interacting Massive
Particles (WIMPs). If discovered, DSs can provide a unique laboratory to test
DM models. DSs are born with a mass of order $M_\odot$ and may grow to a few
million solar masses; in this work we investigate the properties of early DSs
with masses up to $\sim \! 1000 \, M_\odot$, fueled by WIMPS weighing $100$
GeV. We improve the previous implementation of the DM energy source into the
stellar evolution code MESA. We show that the growth of DSs is not limited by
astrophysical effects: DSs up to $\sim \! 1000 \, M_\odot$ exhibit no dynamical
instabilities; DSs are not subject to mass-loss driven by super-Eddington
winds. We test the assumption of previous work that the injected energy per
WIMP annihilation is constant throughout the star; relaxing this assumption
does not change the properties of the DSs. Furthermore, we study DS pulsations,
for the first time investigating non-adiabatic pulsation modes, using the
linear pulsation code GYRE. We find that acoustic modes in DSs of masses
smaller than $\sim \! 200 \, M_\odot$ are excited by the $\kappa-\gamma$ and
$\gamma$ mechanism in layers where hydrogen or helium is (partially) ionized.
Moreover, we show that the mass-loss rates potentially induced by pulsations
are negligible compared to the accretion rates.
