(I) Using state-of-the-art aberration-corrected annular-bright-field (ABF) and high-angle annular-dark-field (HAADF) scanning transmission electron microscopy (STEM), we investigated domain wall structures in multiferroic hexagonal TmMnO3 and LuMnO3 ceramics at atomic scale. Two types of 180 degree domain walls (DWs), i.e. the transverse and the longitudinal DWs (TDWs and LDWs) with uniform displacements of a/3 and 2a/3, respectively, were identified along b direction, which is in consistency with the interlock between ferroelectric and structural translation domain wall predicted previously. (II) Using electron beam as the excitation source to explore the structural evolution of YMnO3, a new phase has been identified under the radiation of electron beam in the transmission electron microscope. Analyses on the electron energy loss spectra reveal that this phase originates from ordered oxygen-vacancy. The first principles calculation was applied to pick out the optimized stable structure with a lower polarization. Analyses of density of states indicate that weak Y-O covalency is favorable for the existence of ferroelectricity, supporting the electrostatic nature of ferroelectricity in the YMnO3-related system.