Measurement of branching fractions, and $CP$ asymmetries in $D^0$ decays are interesting as any difference with respect to the Standard Model prediction would be an indication of new physics. Using the full data sample collected with the Belle detector located at
the KEKB asymmetric-energy $e^+e^-$ (3.5 on 8~GeV) collider, we present the results of the first measurement of $T$-odd moments in the decay $D^{0}\to K_{S}\pi^{+}\pi^{-}\pi^{0}$; measurement of branching fractions and $CP$ asymmetries in $D^{0}\to V\gamma (V = \phi, K^{*0}, \rho^{0} )$, $K_{S}^{0}K_{S}^{0}$ decays; and the first search for $D^0$ decays to invisible final states.