The Belle and Belle II experiments have collected a 1.6 ab$^{-1}$ sample of $e^+e^-$ collision data at center-of-mass energies near the $\Upsilon(4S)$ resonance. These samples contain a large number of $e^+e^-\to c\bar c$ events with production of charmed mesons. We present measurements of $D^0-\bar D^0$ mixing parameters from flavour-tagged $D^0\to K_S^0\pi^+\pi^-$ decays, as well as the most recent $C\!P$ violation searches in $D^0\to K_S^0K_S^0$ decays, and in $D$ meson decays to two or three pions. All these analyses use the 428 fb$^{-1}$ dataset collected by Belle II from 2019 to 2022; the 980 fb$^{-1}$ dataset collected by Belle from 1999 to 2010 is also used when it significantly improves the precision of the measurement.