A theory of non-equilibrium (``shot) noise and high frequency conductance in diffusive mesoscopic conductors with screening is presented. Detailed results are obtained for two simple geometries, for both large and short electron-electron scattering length $l_{ee}$, at frequencies of the order of the inverse Thouless time $1/tau_T$. The conductance and the noise are found to exhibit significant frequency dependence. For $L ll l_{ee}$, the high-frequency ($omegatau_T gg 1$) shot noise spectral density $S_I(omega)$ approaches a finite value between $2eI/3$ and $2eI$, depending on the screening properties of the system, with temperature corrections to $S_I(omega)$ being linear in $T$. However, when $L gg l_{ee}$, $S_I(omega)$ grows as $omega^{1/4}$ (at T=0), is not upper-bound by $2eI$, and has a temperature-dependent component quadratic in $T$. As a result, measurements of $S_I(omega, T)$ can be utilized as a probe of the strength of electron-electron scattering.
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