  The Altshuler-Shklovskii formulas [1] predict, for any disordered quantum
system in the diffusive regime, a universal power law behaviour for the
correlation functions of the mesoscopic eigenvalue density. In this paper and
its companion [2], we prove these formulas for random band matrices. In [2] we
introduced a diagrammatic approach and presented robust estimates on general
diagrams under certain simplifying assumptions. In this paper we remove these
assumptions by giving a general estimate of the subleading diagrams. We also
give a precise analysis of the leading diagrams which give rise to the
Altschuler-Shklovskii power laws. Moreover, we introduce a family of general
random band matrices which interpolates between real symmetric $(\beta=1)$ and
complex Hermitian $(\beta=2)$ models, and track the transition for the
mesoscopic density-density correlation. Finally, we address the higher-order
correlation functions by proving that they behave asymptotically according to a
Gaussian process whose covariance is given by the Altshuler-Shklovskii
formulas.
