We study the effective pair interactions between two charged spherical particles in polyelectrolyte solutions using polymer self-consistent field theory. In a recent study [V. Pryamitsyn and V. Ganesan, Macromolecules 47, 6095 (2015)], we considered a model in which the particles possess fixed charge density, the polymers contain a prespecified amount of dissociated charges and, the dielectric constant of the solution was assumed to be homogeneous in space and independent of the polymer concentration. In this article, we present results extending our earlier model to study situations in which either or both the particle and the polymers possess partially dissociable groups. Additionally, we also consider the case when the dielectric constant of the solution depends on the local concentration of the polymers and when the particle's dielectric constant is lower than that of the solvent. For each case, we quantify the polymer-mediated interactions between the particles as a function of the polymer concentrations and the degree of dissociation of the polymer and particles. Consistent with the results of our previous study, we observe that the polymer-mediated interparticle interactions consist of a short-range attraction and a long-range repulsion. The partial dissociablity of the polymer and particles was seen to have a strong influence on the strength of the repulsive portion of the interactions. Rendering the dielectric permittivity to be inhomogeneous has an even stronger effect on the repulsive interactions and results in changes to the qualitative nature of interactions in some parametric ranges.