We present Hubble Space Telescope (HST) absolute proper motion (PM) measurements for 20 globular clusters (GCs) in the Milky Way (MW) halo at Galactocentric distances $R_{rm GC} approx 10-100$ kpc, with median per-coordinate PM uncertainty 0.06 mas yr$^{-1}$. Young and old halo GCs do not show systematic differences in their 3D Galactocentric velocities, derived from combination with existing line-of-sight velocities. We confirm the association of Arp 2, Pal 12, Terzan 7, and Terzan 8 with the Sagittarius (Sgr) stream. These clusters and NGC 6101 have tangential velocity $V_{rm tan} > 290$ km s$^{-1}$, whereas all other clusters have $V_{rm tan} < 200$ km s$^{-1}$. NGC 2419, the most distant GC in our sample, is also likely associated with the Sgr stream, whereas NGC 4147, NGC 5024, and NGC 5053 definitely are not. We use the distribution of orbital parameters derived using the 3D velocities to separate halo GCs that either formed within the MW or were accreted. We also assess the specific formation history of e.g. Pyxis and Terzan 8. We constrain the MW mass via an estimator that considers the full 6D phase-space information for 16 of the GCs from $R_{rm GC} = 10$ to 40 kpc. The velocity dispersion anisotropy parameter $beta = 0.609^{+0.130}_{-0.229}$. The enclosed mass $M (<39.5 rm{kpc}) = 0.61^{+0.18}_{-0.12} times 10^{12}$ M$_{odot}$, and the virial mass $M_rm{vir} = 2.05^{+0.97}_{-0.79} times 10^{12}$ M$_{odot}$, are consistent with, but on the high side among recent mass estimates in the literature.
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