  In this second paper on the entire virial region of the relaxed fossil
cluster RXJ1159+5531, we present a hydrostatic analysis of the hot intracluster
medium (ICM). For a model consisting of ICM, stellar mass from the central
galaxy (BCG), and an NFW dark matter (DM) halo, we obtain good descriptions of
the projected radial profiles of ICM emissivity and temperature. The BCG
stellar mass is clearly detected with M_star/L_K = 0.61 +/- 0.11 solar,
consistent with stellar population synthesis models for a Milky-Way IMF. We
obtain a halo concentration, c_200 =8.4 +/- 1.0, and virial mass, M_200 = 7.9
+/- 0.6 x 10^13 M_sun. For its mass, the inferred concentration is larger than
most relaxed halos produced in cosmological simulations with Planck parameters,
consistent with RXJ1159+5531 forming earlier than the general halo population.
The baryon fraction at r_200, f_b,200 = 0.134 +/- 0.007, is slightly below the
Planck value (0.155) for the universe. When we account for the stellar baryons
associated with non-central galaxies and the uncertain intracluster light,
f_b,200 increases by ~0.015, consistent with the cosmic value. Performing our
analysis in the context of MOND still requires a large DM fraction (85.0% +/-
2.5% at r=100 kpc) similar to that obtained using the standard Newtonian
approach. The detection of a plausible stellar BCG mass component distinct from
the NFW DM halo in the total gravitational potential suggests that ~10^14 M_sun
represents the mass scale above which dissipation is unimportant in the
formation of the central regions of galaxy clusters. (Abridged)
