Copious production of open-charm mesons and baryons at the LHC, in addition to the flexible trigger scheme, and excellent momentum resolution, impact-parameter, and particle identification capabilities of the LHCb detector, results in some of the most precise measurements to-date on the production and properties of open-charm hadrons. In particular, measurements of the $D_s^{+}$ meson production asymmetry at $\sqrt{s} = 7$ and $8$ TeV, and a high precision measurement of the $\Omega_c^0$ baryon lifetime, are presented. These measurements provide valuable information to tune event generators, on non-perturbative and spectator quark effects in $\Omega_c^0$ baryon decays, and provide valuable input to future LHCb measurements.