  In this work, we study the chemical compositions and kinematic properties of
six metal-poor stars with [Fe/H] $< -2.5$ in the Galactic halo. From
high-resolution (R $\sim$~110,000) spectroscopic observations obtained with the
Lick/APF, we determined individual abundances for up to 23 elements, to
quantitatively evaluate our sample. We identify two carbon-enhanced metal-poor
stars (J1630+0953 and J2216+0246) without enhancement in neutron-capture
elements (CEMP-no stars), while the rest of our sample stars are
carbon-intermediate. By comparing the light-element abundances of the CEMP
stars with predicted yields from non-rotating zero-metallicity massive-star
models, we find that possible the progenitors of J1630+0953 and J2216+0246
could be in the 13-25 M$_{\odot}$ mass range, with explosion energies 0.3-1.8$
\times 10^{51}$ erg. In addition, the detectable abundance ratios of light and
heavy elements suggest that our sample stars are likely formed from a
well-mixed gas cloud, which is consistent with previous studies. We also
present a kinematic analysis, which suggests that most of our program stars
likely belong to the inner-halo population, with orbits passing as close as
$\sim$ 2.9 kpc from the Galactic center. We discuss the implications of these
results on the critical constraints on the origin and evolution of CEMP stars,
as well as the nature of the Population III progenitors of the lowest
metallicity stars in our Galaxy.
