The kinetics of the bimolecular A+B-->0 reaction between charged reactants is studied in two dimensions, i.e., on a surface. The theory is based on the Kirkwood superposition approximation for three-particle densities and the self-consistent treatment of the electrostatic interactions defined by the non-uniform spatial distribution of similar and dissimilar reactants. Special attention is paid to pattern formation and many-particle effects arising from reaction-induced formation of loose domains containing similar reactants only. It is shown that the critical exponent ct characterizing the algebraic concentration decay law, n(t) proportional to t(-alpha), differs strongly between symmetric (D-A = D-B) and asymmetric (D-A = 0) reactant mobilities. This effect is abnormal from the point of view of standard chemical kinetics. It arises directly from the specific spatial distribution in the system as in "raisins A in a dough B." At long reaction times the asymptotics of the interaction potentials is of non-equilibrium type at large relative distances. The accumulation kinetics in the presence of a permanent source is studied. Results of the microscopic formalism are compared with a previous mesoscopic theory.