  The process $\pi N\to e^+e^- N$ (IPE), being a natural and unique laboratory
for studying the hadron electromagnetic structure in the
sub-$N\bar{N}$-threshold time-like region of the virtual-photon ``mass''
$\lambda^2$, turns out to be also very useful for investigating the nucleon
weak structure. A theoretical basis of the methods for extracting practically
model-independent values of the electromagnetic hadron form factors in the
time-like region and for determining the weak structure of the nucleon in the
space-like region from experimental data on IPE at low energies is outlined.
The results of extracting, by those methods, the electromagnetic
$F_1^v(\lambda^2)$ and pseudoscalar $G_P(t)$ form-factors of a nucleon are
presented, where an indication of the existence of the state $\pi^\p$ in the
range 500-800 MeV (possibly the first radial excitation of pion) is obtained,
and the coupling constant of this new state with the nucleon is estimated.
