  Using the leading twist approach to nuclear shadowing, which is based on the
relationship between nuclear shadowing and diffraction on a nucleon, we
calculate next-to-leading order nuclear parton distribution functions (nPDFs)
and structure functions in the region $0.2 > x > 10^{-5}$ and $Q^2 \geq 4$
GeV$^2$.
  The uncertainties of our predictions due the uncertainties of the
experimental input and the theory are quantified. We determine the relative
role of the small ($\sim Q^2$) and large ($\gg Q^2$) diffractive masses in
nuclear shadowing as a function of $x$ and find that the large mass
contribution, which is an analog of the triple Pomeron exchange, becomes
significant only for $x \le 10^{-4}$. Comparing our predictions to the
available fixed-target nuclear DIS data, we argue, based on the current
experimental studies of the leading twist diffraction, that the data at
moderately small $x\sim 0.01$ and $Q^2 \sim 2$ GeV$^2$ could contain
significant higher twist effects hindering the extraction of nPDFs from that
data. Also, we find that the next-to-leading order effects in nuclear shadowing
in the ratio of the nucleus to nucleon structure functions $F_2$ are quite
sizable. Within the same formalism, we also present results for the impact
parameter dependence of nPDFs. We also address the problem of extracting of the
neutron
  $F_{2n}(x,Q^2)$ from the deuteron and proton data. We suggest a simple and
nearly model-independent procedure of correcting for nuclear shadowing effects
using $F_2^A/F_2^D$ ratios.
