The pair-interactions Uij (r) determine the thermodynamics and linear transport properties of matter via the pair-distribution functions (PDFs), i.e., gij(r). Great simplicity is achieved if Uij (r) could be directly used to predict material properties via classical simulations, avoiding many-body wavefunctions. Warm dense matter (WDM) is encountered in quasi-equilibria where the electron temperature Te differs from the ion temperature Ti, as in laser-heated or in shock-compressed matter. The electron PDFs gee(r) as perturbed by the ions are used to evaluate fully non-local exchangecorrelation corrections to the free energy, using Hydrogen as an example. Electron-ion potentials for ions with a bound core are discussed with Al and Si as examples, for WDM with Te = Ti, and valid for times shorter than the electron-ion relaxation time. In some cases the potentials develop attractive regions, and then become repulsive and 'Yukawa-like' for higher Te. These results clarify the origin of initial phonon-hardening and rapid release. Pair-potentials for shock-heated WDM show that phonon hardening would not occur in most such systems. Defining meaningful quasi-equilibrium static transport coefficients consistent with the dynamic values is addressed. There seems to be no meaningful 'static conductivity' obtainable by extrapolating experimental or theoretical σ(ω, Ti, Te) to ω → 0, unless Ti → Te as well. Illustrative calculations of quasi-static resistivities R(Ti, Te) of laser-heated as well as shock-heated Aluminum and Silicon are presented using our pseudopotentials, pair-potentials and classical integral equations. The quasi-static resistivities display clear differences in their temperature evolutions, but are not the strict ω → 0 limits of the dynamic values.