  Based on the {\it ab-initio} band structure for Na$_x$CoO$_2$ we derive the
single-electron energies and the effective tight-binding description for the
$t_{2g}$ bands using projection procedure. Due to the presence of the
next-nearest-neighbor hoppings a local minimum in the electronic dispersion
close to the $\Gamma$ point of the first Brillouin zone forms. Correspondingly,
in addition to a large Fermi surface an electron pocket close to the $\Gamma$
point emerges at high doping concentrations. The latter yields the new
scattering channel resulting in a peak structure of the itinerant magnetic
susceptibility at small momenta. This indicates dominant itinerant in-plane
ferromagnetic fluctuations above certain critical concentration $x_m$, in
agreement with neutron scattering data. Below $x_m$ the magnetic susceptibility
shows a tendency towards the antiferromagnetic fluctuations. We further analyze
the many-body effects on the electronic and magnetic excitations using various
approximations applicable for different $U/t$ ratio.
