  This is a second study of chiral anomaly induced transport within a
holographic model consisting of anomalous $U(1)_V\times U(1)_A$ Maxwell theory
in Schwarzschild-$AdS_5$ spacetime. In the first part, chiral
magnetic/separation effects (CME/CSE) are considered in presence of a static
spatially-inhomogeneous external magnetic field. Gradient corrections to
CME/CSE are analytically evaluated up to third order in the derivative
expansion. Some of the third order gradient corrections lead to an
anomaly-induced negative $B^2$-correction to the diffusion constant. We also
find non-linear in $B$ modifications to the chiral magnetic wave (CMW). In the
second part, we focus on the experimentally interesting case of the axial
chemical potential being induced dynamically by a constant magnetic and
time-dependent electric fields. Constitutive relations for the vector/axial
currents are computed employing two different approximations: (a) derivative
expansion (up to third order) but fully nonlinear in the external fields, and
(b) weak electric field limit but resuming all orders in the derivative
expansion. A non-vanishing non-linear axial current (CSE) is found in the first
case. Dependence on magnetic field and frequency of linear transport
coefficient functions (TCFs) is explored in the second.
