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 ∼100 kpc. We use a class of global mass-estimators (from Paper I), obtaining mass measurements at different locations. M87's DM fraction changes from ≈0.2 at the starlight's effective radius (6 kpc) to ≈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+1.5−2.0×1011M⊙ and the DM within 135 kpc as 8.0+1.0−4.0×1012M⊙. The inner DM density behaves as ρ∼r−γ with γ≈1.6. This is steeper than the cosmologically preferred cusp ρ∼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.