  A method for calculating the electronic levels in the compact superheavy
nuclear quasi-molecules, based on solving the two-center Dirac equation using
the multipole expansion of two-center potential, is developed. For the
internuclear distances up to $d\sim100$~fm such technique reveals a quite fast
convergence and allows for computing the electronic levels in such systems with
accuracy $\sim 10^{-6} $. The critical distances $R_{cr}$ between the nuclei
for $1\sigma_g$ and $1\sigma_u$ electronic levels in the region $Z\simeq
87-100$ are calculated. By means of the same technique the shifts of electronic
levels due to the effective interaction $\Delta U_{AMM}$ of the electron's
magnetic anomaly with the Coulomb field of the closely spaced heavy nuclei are
evaluated as a function of the internuclear distance and the charge of the
nuclei, non-perturbatively both in $Z\alpha$ and (partially) in $\alpha/\pi$.
It is shown, that the levels shifts near the lower continuum decrease with the
enlarging size of the system of Coulomb sources both in the absolute units and
in units of $Z^4 \alpha^5 / \pi n^3$. The last result is generalized to the
whole self-energy contribution to the level shifts and so to the possible
behavior of radiative part of QED-effects with virtual photon exchange near the
lower continuum in the overcritical region.
