The effects of adsorbate lateral interactions on the kinetics of surface diffusion and desorption are studied by means of kinetic and thermodynamic Monte Carlo simulations. This study is motivated by recent diffusion and desorption experiments on the NH3/Re(001) system, which show that the activation energies of these processes decrease (in different fashions) with increasing surface coverage, the interactions between the adsorbates are thus assumed to be repulsive. A long range dipole-dipole-like potential is used to simulate both the diffusion and desorption processes. Most calculations are carried out with the interaction range extending up to fourth-order neighbors. Longer ranges are found to barely affect the kinetic behavior. On the other hand, shorter ranges of interaction result in qualitatively and quantitatively different structural (thermodynamic phase) behaviors and, consequently, in very different kinetics of diffusion and desorption. The model used to calculate diffusion kinetics assumes that the activation barrier to particle diffusion depends, simultaneously, on the local environments of both the initial and the final sites involved in the elementary event of particle jumps. The chemical diffusion coefficient is evaluated based on thermodynamic and kinetic Monte Carlo simulations. It is found to increase with surface coverage, reflecting the repulsive nature of the interactions. Yet, unlike the experimental results, the increase is nonmonotonic but rather, somewhat oscillatory-reflecting the structural phase transitions of the adsorbed layer. The activation energy of desorption is found to decrease by about 15 kcal/mole as the coverage increases from 0 to 1, showing steeper slopes around the coverages corresponding to a perfectly ordered adlayer phase. These results are in satisfactory qualitative and quantitative agreement with experiment. Finally, it is shown that the coverage dependence of the activation barrier to diffusion can be reasonably well evaluated from equilibrium thermodynamic desorption data.