Electrostatic interaction and hindered diffusion of ion-penetrable spheres in a slit pore filled with an electrolyte solution are investigated theoretically. The concentration of the particles is assumed sufficiently low so that the interactions between the particles can be neglected. The slit pore comprises two parallel infinite plates, which can be either permeable or impermeable to the electrolyte. The electrostatic interaction energy is obtained analytically by adopting an integral of Green's function and an image method. It is found that for impermeable plates having constant surface charge densities, the electrostatic interaction can be attractive or repulsive for a particle with charge of opposite sign, depending on the relative magnitudes of charge densities and particle location. Similar behavior is predicted for plates with constant surface potential and a particle with charge of like sign. The interaction energy is used to determine the spatial distribution of the particle in the pore and the partition coefficient, and then to calculate the average and apparent diffusivities. The average diffusivity calculated from the average mobility in the pore is always smaller than that in the bulk solution because of greater drag the particle experiences in the presence of the plates. This mean diffusivity is larger than that in the corresponding neutral system for repulsive electrostatic interaction, but becomes smaller for attractive interaction. The apparent diffusivity defined from the flux based on the bulk concentration of the particle depends strongly on the ion concentration, as does the partition coefficient when the double layer is sufficiently thick.