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Using the leading twist approach to nuclear shadowing, which is based on therelationship between nuclear shadowing and diffraction on a nucleon, wecalculate 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 theexperimental input and the theory are quantified. We determine the relativerole of the small ($\sim Q^2$) and large ($\gg Q^2$) diffractive masses innuclear shadowing as a function of $x$ and find that the large masscontribution, which is an analog of the triple Pomeron exchange, becomessignificant only for $x \le 10^{-4}$. Comparing our predictions to theavailable fixed-target nuclear DIS data, we argue, based on the currentexperimental studies of the leading twist diffraction, that the data atmoderately small $x\sim 0.01$ and $Q^2 \sim 2$ GeV$^2$ could containsignificant higher twist effects hindering the extraction of nPDFs from thatdata. Also, we find that the next-to-leading order effects in nuclear shadowingin the ratio of the nucleus to nucleon structure functions $F_2$ are quitesizable. Within the same formalism, we also present results for the impactparameter dependence of nPDFs. We also address the problem of extracting of theneutron  $F_{2n}(x,Q^2)$ from the deuteron and proton data. We suggest a simple andnearly model-independent procedure of correcting for nuclear shadowing effectsusing $F_2^A/F_2^D$ ratios.Comment: 42 pages, 18 figures, 1 table, RevTex. The final version published in  PRD 71, 054001 (2005

Leading twist nuclear shadowing: Uncertainties, comparison to experiments, and higher twist effects