The metal-insulator transition and conductivity are studied in the half-filled ionic Hubbard model. The static and dynamics charge susceptibility are calculated in the framework of the t-J-V model. For a sufficiently strong intersite Coulomb repulsion the charge density waves arise in the system. Using the memory function formalism the dispersion of low-energy charge excitations is considered. A microscopic theory of superconductivity in the extended t-J-V model accounting for intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The d-wave pairing with high-Tc mediated by spin fluctuations induced by strong kinematic interaction for the Hubbard operators is found. Contributions to the d-wave pairing from intersite Coulomb repulsion and phonons turned out to be small.

(based on the Ph.D. thesis)