  We use the Fisher information matrix to investigate the angular resolution
and luminosity distance uncertainty for coalescing binary neutron stars (BNSs)
and neutron star-black hole binaries (NSBHs) detected by the third-generation
(3G) gravitational-wave (GW) detectors. Our study focuses on an individual 3G
detector and a network of up to four 3G detectors at different locations
including the US, Europe, China and Australia for the proposed Einstein
Telescope (ET) and Cosmic Explorer (CE) detectors. We in particular examine the
effect of the Earth's rotation, as GW signals from BNS and low mass NSBH
systems could be hours long for 3G detectors. We find that, a time-dependent
antenna beam-pattern function can help better localize BNS and NSBH sources,
especially those edge-on ones. The medium angular resolution for one ET-D
detector is around 150 deg$^2$ for BNSs at a redshift of $z=0.1$. The medium
angular resolution for a network of two CE detectors in the US and Europe
respectively is around 20 deg$^2$ at $z=0.2$ for the simulated BNS and NSBH
samples. While for a network of two ET-D detectors, the similar angular
resolution can be achieved at a much higher redshift of $z=0.5$. The angular
resolution of a network of three detectors is mainly determined by the
baselines between detectors regardless of the CE or ET detector type. We
discuss the implications of our results to constrain the Hubble constant $H_0$,
the deceleration parameter $q_0$ and the equation-of-state (EoS) of dark
energy. We find that in general, if 10 BNSs or NSBHs at $z=0.1$ with known
redshifts are detected, $H_0$ can be measured with an accuracy of $0.9\%$. If
1000 face-on BNSs at $z<2$ are detected with known redshifts, we are able to
achieve $\Delta q_0=0.002$, or $\Delta w_0=0.03$ and $\Delta w_a=0.2$ for dark
energy.(Abridged version).
