We present a detailed study of the faint Milky Way satellite Draco II (Dra II) from deep CFHT/MegaCam broadband $g$ and $i$ photometry and narrow-band metallicity-sensitive CaHK observations, along with follow-up Keck II/DEIMOS multi-object spectroscopy. Forward modeling of the deep photometry allows us to refine the structural and photometric properties of Dra II: the distribution of stars in colour-magnitude space implies Dra II is old (13.5 $ pm 0.5 $ Gyr), very metal poor, very faint ($ L_V = 180 ^{+124}_{-72} L_odot $), and at a distance $d = 21.5 pm 0.4$ kpc. The narrow-band, metallicity-sensitive CaHK Pristine photometry confirms this very low metallicity ([Fe/H]$ = -2.7 pm 0.1$ dex). Even though our study benefits from a doubling of the spectroscopic sample size compared to previous investigations, the velocity dispersion of the system is still only marginally resolved ($sigma_{vr}<5.9$ km s$^{-1}$ at the 95 per cent confidence level) and confirms that Dra II is a dynamically cold stellar system with a large recessional velocity ($langle v_{r}rangle = -342.5^{+1.1}_{-1.2} $ km s$^{-1}$). We further show that the spectroscopically confirmed members of Dra~II have a mean proper motion of $(mu_alpha^*,mu_delta)=(1.26 pm 0.27,0.94 pm 0.28) $ mas yr$^{-1}$ in the Gaia DR2 data, which translates to an orbit with a pericenter and an apocenter of $21.3 ^{+0.7}_{-1.0}$ and $153.8 ^{+56.7}_{-34.7}$ kpc, respectively. Taken altogether, these properties favour the scenario of Dra~II being a potentially disrupting dwarf galaxy. The low-significance extra-tidal features we map around the satellite tentatively support this scenario.
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