We present the leading logarithmic QCD corrections to the matrix element of the decay b --> de(+)e(-) in the two Higgs doublet model with tree level flavor changing currents (model III). We continue studying the differential branching ratio and the CP-violating asymmetry for the exclusive decays B --> pi e(+)e(-) and B --> pe(+)e(-) and analysing the dependencies of these quantities on the selected model III parameters, xi(U,D), including the leading logarithmic QCD corrections. Further, we present the forward-backward asymmetry of dileptons for the decay B --> pe(+)e(-) and discuss the dependencies to the model III parameters. We observe that there is a possibility to enhance the branching ratios and suppress the CP-violating effects for both decays in the framework of the model III. Therefore, the measurements of these quantities will he an efficient tool to search the new physics beyond the SM.