  A proper understanding of the Milky Way (MW) dwarf galaxies in a cosmological
context requires knowledge of their 3D velocities and orbits. However, proper
motion (PM) measurements have generally been of limited accuracy and available
only for more massive dwarfs. We therefore present a new study of the
kinematics of the MW dwarf galaxies. We use the Gaia DR2 for those dwarfs that
have been spectroscopically observed in the literature. We derive systemic PMs
for 39 galaxies and galaxy candidates out to 420 kpc, and generally find good
consistency for the subset with measurements available from other studies. We
derive the implied Galactocentric velocities, and calculate orbits in canonical
MW halo potentials of "low" ($0.8 \times 10^{12} M_\odot$) and "high" mass
($1.6 \times 10^{12} M_\odot$). Comparison of the distributions of orbital
apocenters and 3D velocities to the halo virial radius and escape velocity,
respectively, suggests that the satellite kinematics are best explained in the
high-mass halo. Tuc III, Crater II, and additional candidates have orbital
pericenters small enough to imply significant tidal influences. Relevant to the
missing satellite problem, the fact that fewer galaxies are observed to be near
apocenter than near pericenter implies that there must be a population of
distant dwarf galaxies yet to be discovered. Of the 39 dwarfs: 12 have orbital
poles that do not align with the MW plane of satellites (given reasonable
assumptions about its intrinsic thickness); 10 have insufficient PM accuracy to
establish whether they align; and 17 satellites align, of which 11 are
co-orbiting and (somewhat surprisingly, in view of prior knowledge) 6 are
counter-orbiting. Group infall might have contributed to this, but no
definitive association is found for the members of the Crater-Leo group.
