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We investigate a one--dimensional wire of interacting electrons connected toone--dimensional noninteracting leads in the absence and in the presence of abackscattering potential. The ballistic wire separates the charge and spinparts of an incident electron even in the noninteracting leads. The Fouriertransform of nonlocal correlation functions are computed for $T\gg \omega$. Inparticular, this allows us to study the proximity effect, related to theAndreev reflection. A new type of proximity effect emerges when the wire hasnormally a tendency towards Wigner crystal formation. The latter is suppressedby the leads below a space--dependent crossover temperature; it gets dominatedeverywhere by the $2k_F$ CDW at $T<L^{3/2 (K-1)}$ for short range interactionswith parameter $K<1/3$. The lowest--order renormalization equations of a weakbackscattering potential are derived explicitly at finite temperature. Aperturbative expression for the conductance in the presence of a potential witharbitrary spatial extension is given. It depends on the interactions, but isalso affected by the noninteracting leads, especially for very repulsiveinteractions, $K<1/3$. This leads to various regimes, depending on temperatureand on $K$. For randomly distributed weak impurities, we compute theconductance fluctuations, equal to that of $R=g-2e^2 /h$. While the behavior of$Var(R)$ depends on the interaction parameters, and is different for electronswith or without spin, and for $K<1/3$ or $K>1/3$, the ratio $Var(R)/R^2$ staysalways of the same order: it is equal to $L_T/L\ll 1$ in the high temperaturelimit, then saturates at 1/2 in the low temperature limit, indicating that therelative fluctuations of $R$ increase as one lowers the temperature.Comment: 24 two-column revtex pages, five postscript figures. This paper is an  extended version of cond-mat/961217

Interacting electrons with spin in a one-dimensional dirty wire connected to leads