Structural and thermodynamic properties of ionic fluids are related to those of a simpler "mimic" system with short ranged intermolecular interactions in a spatially varying effective field by use of Local Molecular Field (LMF) theory, already successfully applied to nonuniform simple fluids. By consistently using the LMF approximation to describe only the slowly varying part of the Coulomb interaction, which we view as arising from a rigid Gaussian charge distribution with an appropriately chosen width σ, exceptionally accurate results can be found. In this paper we study a uniform system of charged hard spheres in a uniform neutralizing background, where these ideas can be presented in their simplest form. At low densities the LMF theory reduces to a generalized version of the Poisson-Boltzmann approximation, but the predicted structure factor satisfies the exact StillingerLovett moment conditions, and with optimal choice of σ the lowest order approximation remains accurate for much stronger couplings. At high density and strong couplings the pair correlation function in the uniform mimic system with short ranged interactions is very similar to that of the full ionic system. A simple analytic formula can then describe the difference in internal energy between the ionic system and the associated mimic system.

A metastable state, characterized by a low degree of mass localization, is identified using density-functional theory (DFT). This free energy minimum, located through the proper evaluation of competing terms in the free energy functional, is independent of the specific form of the DFT used. Computer simulation results on particle motion indicate that this heterogeneous state corresponds to the deeply supercooled state.

Effective attraction between like-charged walls mediated by counterions is studied using local molecular field (LMF) theory. Monte Carlo simulations of the "mimic system" given by LMF theory, with short-ranged "Coulomb core" interactions in an effective single particle potential incorporating a mean-field average of the long-ranged Coulomb interactions, provide a direct test of the theory, and are in excellent agreement with more complex simulations of the full Coulomb system by Moreira and Netz [Eur. Phys. J. E 8, 33 (2002)]. A simple, generally applicable criterion to determine the consistency parameter sigma(min) needed for accurate use of the LMF theory is presented.

The empirical relation (D(*))(alpha) = a exp[S] between the self-diffusion coefficient D(*) and the excess entropy S of a liquid is studied here in the context of theoretical model calculation. The coefficient alpha is dependent on the interaction potential and shows a crossover at an intermediate density, where cooperative dynamics become more important. Around this density a departure from the Stokes-Einstein relation is also observed. The above relation between entropy and diffusion is also tested for the scaled total diffusion coefficient in a binary mixture.

The free energy of the supercooled liquid near freezing is studied in the density-functional approach using the modified weighted density approximation. A class of minima corresponding to heterogeneous structures characterized by weak mass localization are detected. The stability of these structures is found to be greater than the highly localized "hard-sphere glass" state in the intermediate density range above freezing.