We extend the formalism of weak interaction processes, obtaining newexpressions for the transition rates, which greatly facilitate numerical calculations, for both neutrino- nucleus reactions and muon capture. Explicit violation of the conserved vector current hypothesis by the Coulomb field, as well as development of a sum-rule approach for inclusive cross sections, has been worked out. We have done a thorough study of exclusive (ground-state) properties of 12B and 12N within the projected quasiparticle random phase approximation (PQRPA). Good agreement with experimental data achieved in this way put into evidence the limitations of the standard RPA and QRPA models, which come from the inability of the RPA to open the p3/2 shell and from the nonconservation of the number of particles in the QRPA. The inclusive neutrino/antineutrino (ν/˜ν) reactions 12C(ν, e−)12N and 12C(˜ν, e+)12B are calculated within both the PQRPA and the relativistic QRPA. It is found that (i) the magnitudes of the resulting cross sections are close to the sum-rule limit at low energy, but significantly smaller than this limit at high energies, for both ν and ˜ν ; (ii) they increase steadily when the size of the configuration space is augmented, particularly for ν/˜ν energies >200 MeV ; and (iii) they converge for sufficiently large configuration space and final-state spin. The quasi-elastic 12C(ν, μ −)12N cross section recently measured in the MiniBooNE experiment is briefly discussed. We study the decomposition of the inclusive cross section based on the degree of forbiddenness of different multipoles. A few words are dedicated to the ν/˜ν-12C charge-exchange reactions related to astrophysical applications.