We investigate ionic criticality on the basis of a specially devised spherical model that accounts both for Coulomb and nonionic forces in binary systems. We show in detail here the consequences of the entanglement of density and charge correlation functions GNN and GZZ on criticality and screening. We also show on this soluble model how, because of electroneutrality, the long-range Coulomb interactions do not change the universality class of criticality in the model driven primarily by sufficiently attractive non-ionic interactions. Near criticality, GNN and GZZ are fully decoupled in charge symmetric systems. However, in more realistic nonsymmetric models, charge and density fluctuations couple in leading order so that the charge and density correlation lengths diverge asymptotically in a similar way. Similarly, the Stillinger-Lovett sum-rule, which characterizes a conducting fluid, is violated at criticality in non-symmetric models when the critical-point density-decay exponent η vanishes. In addition, if quantum effects are accounted for semi-classically by incorporating algebraically decaying interactions, GZZ decays only as a power law in the whole phase space, contrary to the usually expected exponential Debye screening. We expect these results on this soluble toy model to be general and to reveal general mechanisms ruling ionic criticality.