The data from the Gaia satellite led us to revise our conception of the Galaxy structure and history. Hitherto unknown components have been discovered and a deep re-thinking of what the Galactic halo is is in progress.} We selected from the Gaia catalogue stars with extreme transverse velocities with respect to the Sun (|VT|>500km/s) and observed them with FORS2 at the ESO VLT, to classify them using both their chemical and dynamical properties. Two apparently young stars, identified in paper I (Caffau et al., 2020A&A...638A.122C, Cat. J/A+A/638/A122), were observed with UVES. We derived abundances for Na, Mg, Ca, Ti, Mn, and Fe, analysing the spectra with MyGIsFOS, while for Ba we used line profile fitting. We computed actions from parallaxes and kinematical data. The stars span the metallicity range -3.5<=[Fe/H]<=-0.5 with <[Fe/H]>=-1.6. Star GHS143 has a total speed of about 1440km/s, which is almost three times faster than the local escape velocity of 522km/s, strongly implying this star is unbound to the Galaxy. Remarkably, this star is not escaping from the Galaxy, but it is falling into it. Ten stars are apparently young with masses in excess of 1.3M_{sun}_. Their interpretation as evolved blue stragglers is doubtful. The existence of a young metal-poor population is possible. The two stars observed with UVES show no lithium, suggesting they are blue stragglers. We detected a metal-poor population, confined to the bulge, that we call SpiteF, and argue that it is the result of a recent accretion event. We detect 102 candidates of the Aurora population that should have formed prior to the formation of the disc. Our sample is non-homogeneous and mainly retrograde. The stars are metal poor, and 23% have [Fe/H]<=-2.0. Our selection is efficient at finding very metal-poor stars, but it selects peculiar populations.