Data of the Borexino experiment on the detection of the reaction involving elastic solar-neutrino scattering on an electron are presented. The fraction of electron neutrinos in the fluxes of 7Be and 8B neutrinos is in agreement with the LMA MSW oscillation solution. The uniquely low level of the Borexino detector background made it possible to set new limits on the effective magnetic moment of the neutrino, on the possible violation of the Pauli exclusion principle, and on some other rare processes.