Phys. Rev. D 109, 112002 (2024) The cross section of the process $e^+e^-\to\pi^+\pi^-$ has been measured in the center of mass energy range from 0.32 to 1.2 GeV with the CMD-3 detector at the electron-positron collider VEPP-2000. The measurement is based on a full dataset collected below 1 GeV during three data taking seasons, corresponding to an integrated luminosity of about 62 pb$^{-1}$. In the dominant $\rho$-resonance region, a systematic uncertainty of 0.7% has been reached. At energies around $\phi$-resonance the $\pi^+\pi^-$ production cross section was measured for the first time with high beam energy resolution. The forward-backward charge asymmetry in the $\pi^+\pi^-$ production has also been measured. It shows a strong deviation from the theoretical prediction based on the conventional scalar quantum electrodynamics framework, and it is in good agreement with the generalized vector-meson-dominance and dispersive-based predictions. The impact of the presented results on the evaluation of the hadronic contribution to the anomalous magnetic moment of muon is discussed.