A comprehensive study of the electronic structure, thermodynamic and electrical transport properties reveals the existence of inhomogeneous superconductivity due to structural disorder in Ca3Rh4Sn13 doped with La (Ca3−xLaxRh4Sn13) or Ce (Ca3−xCexRh4Sn13) with superconducting critical temperatures T c higher than those (Tc) observed in the parent compounds. The T − x diagrams and the entropy S(x)T isotherms document well the relation between the degree of atomic disorder and separation of the high-temperature T c and Tc-bulk phases. In these dirty superconductors, with the mean free path much smaller than the coherence length, the Werthamer-Helfand-Hohenber theoretical model does not fit well the Hc2(T) data. We demonstrate that this discrepancy can result from the presence of strong inhomogeneity or from two-band superconductivity in these systems. Both the approaches very well describe the H − T dependencies, but the present results as well as our previous studies give stronger arguments for the scenario based on the presence of nanoscopic inhomogeneity of the superconducting state. A comparative study of La-doped and Ce-doped Ca3Rh4Sn13 showed that in the disordered Ca3−xCexRh4Sn13 alloys the presence of spin-glass effects is the cause of the additional increase of T c in respect to the critical temperatures of disordered Ca3−xLaxRh4Sn13. We also revisited the nature of structural phase transition at T ∼ 130 170 K and documented that there might be another precursor transition at higher temperatures. Raman spectroscopy and thermodynamic properties suggest that this structural transition may be associated with a CDW-type instability.