$CP$ violation in charm meson decays is expected to be small within the Standard Model (SM) framework, and an observation of a large $CP$ asymmetry could indicate new physics. We report measurement of branching fractions and direct $CP$ asymmetries $A_{CP}$ in $D^{0} \to \pi^+\pi^-\eta,\, K^+K^-\eta,\, \phi \eta$ and $D^{0} \to K^{0}_{S}K^{0}_{S}\pi^{+}\pi^{-}$ decays. For the latter the T-odd asymmetry $a_{CP}^{T}$, sensitive to $CP$ violation in the decay, is also measured. This report also covers the search for $CP$ violation in $D \to K h \pi \pi^{0}$ $(h = \pi, K)$ decays. The results are based on the full data collected with the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider.