||The CePd1-xRhx alloy exhibits a continuous evolution from ferromagnetism (T-C=6.5 K) at x=0 to a mixed-valence (MV) state at x=1. We have performed a detailed investigation on the suppression of the ferromagnetic (F) phase in this alloy using dc (chi(dc)) and ac (chi(ac)) susceptibility, specific heat (C-m), resistivity (rho), and thermal expansion (beta) techniques. Our results show a continuous decrease of T-C(x) with negative curvature down to T-C=3 K at x(*)=0.65, where a positive curvature takes over. Beyond x(*), a cusp in chi(ac) is traced down to T-C(*)=25 mK at x=0.87, locating the critical concentration between x=0.87 and 0.90. The quantum criticality of this region is recognized by the -log(T/T-0) dependence of C-m/T, which transforms into a T-q (q approximate to 0.5) one at x=0.87. At high temperature, this system shows the onset of valence instability revealed by a deviation from Vegard's law (at x(V)approximate to 0.75) and increasing hybridization effects on high-temperature chi(dc) and rho(T). Coincidentally, a Fermi liquid contribution to the specific heat (gamma) arises from the MV component, which becomes dominant at the CeRh limit. In contrast to antiferromagnetic systems, no C-m/T flattening is observed for x > x(cr) but, rather, the mentioned power-law divergence, which coincides with a change of sign of beta(T). The coexistence of F and MV components and the sudden changes in the T dependencies are discussed in the context of randomly distributed magnetic and Kondo couplings.