The Pristine survey -- XII: Gemini-GRACES chemo-dynamical study of newly discovered extremely metal-poor stars in the Galaxy

High-resolution optical spectra of 30 metal-poor stars selected from the \textit{Pristine} survey are presented, based on observations taken with the Gemini Observatory GRACES spectrograph. Stellar parameters T$_{\rm eff}$ and $\log g$ are determined using Gaia DR2 parallaxes and MIST/MESA metal-poor isochrones. GRACES spectra are used to determine chemical abundances (or upper-limits) for 20 elements (Li, O, Na, Mg, K, Ca, Ti, Sc, Cr, Mn, Fe, Ni, Cu, Zn, Y, Zr, Ba, La, Nd, Eu). These stars are confirmed to be metal-poor ([Fe/H]$<-2.5$), with higher precision than from earlier medium-resolution analyses. The chemistry for most targets is similar to that of other extremely metal-poor stars in the Galactic halo. Two stars near [Fe/H]$=-3.0$ have unusually low Ca and high Mg, suggestive of contributions from few SN~II, where alpha-element formation through hydrostatic nucleosynthesis was more efficient. Three new carbon-enhanced metal-poor stars are also identified (two CEMP-s and one potential CEMP-no star), when our chemical abundances are combined with carbon from previous medium-resolution analyses. The GRACES spectra also provide precision radial velocities ($\sigma_{\rm RV}\le0.2$ km s$^{-1}$) for dynamical orbit calculations with the Gaia DR2 proper motions. Most of our targets are dynamically associated with the Galactic halo; however, five stars with [Fe/H]$<-3$ have planar-like orbits, including one retrograde planar star. Another five stars are dynamically consistent with the Gaia-Sequoia accretion event; three have typical high [$\alpha$/Fe] ratios for their metallicities, whereas two are [Mg/Fe]-deficient, and one is a new CEMP-s candidate. These results are discussed in terms of the formation and early chemical evolution of the Galaxy.