  We study the Globular Cluster (GC) system of the nearby elliptical galaxy M87
using the newly available dataset with accurate kinematics (Strader et
al.2011). We find evidence for three distinct sub-populations of GCs in terms
of colours, kinematics and radial profiles. We show that a decomposition into
three populations (blue, intermediate and red GCs) is statistically preferred
to one with two or four populations, and relate them to the stellar profile. We
exploit the sub-populations to derive dynamical constraints on the mass and
Dark Matter (DM) content of M87 out to $\sim100$ kpc. We use a class of global
mass-estimators (from Paper I), obtaining mass measurements at different
locations. M87's DM fraction changes from $\approx$0.2 at the starlight's
effective radius (6 kpc) to $\approx$0.95 at the distance probed by the most
extended, blue GCs (135 kpc). We supplement this with \textit{virial
decompositions}, exploiting the dynamical model to produce a separation into
multiple components. These yield the luminous mass as $5.5^{+1.5}_{-2.0}\times
10^{11}M_\odot$ and the DM within 135 kpc as $8.0^{+1.0}_{-4.0}\times
10^{12}M_\odot.$ The inner DM density behaves as $\rho \sim r^{-\gamma}$ with
$\gamma\approx 1.6$. This is steeper than the cosmologically preferred cusp
$\rho \sim r^{-1},$ providing evidence of DM contraction. Finally, we combine
the GC separation into three sub-populations and the Jeans equations, obtaining
information on the orbits of the GC system. The centrally concentrated red GCs
exhibit tangential anisotropy, consistent with radial-orbit depletion by tidal
shredding. The most extended blue GCs have an isotropic velocity dispersion
tensor in the central parts, which becomes more tangential moving outwards,
consistent with adiabatic contraction of the DM halo.
