  Determining for the first time the Darwin operator contribution for the
non-leptonic charm-quark decays and using new non-perturbative results for the
matrix elements of $\Delta C=0$ four-quark operators, including
eye-contractions, we present a comprehensive study of the lifetimes of charmed
mesons and inclusive semileptonic decay rates as well as the ratios, within the
framework of the Heavy Quark Expansion (HQE). We find good agreement with
experiment for the ratio $\tau(D^+)/\tau(D^0)$, for the total $D_s^+$-meson
decay rate, for the semileptonic rates of all three mesons $D^0$, $D^+$ and
$D_s^+$, and for the semileptonic ratio $\Gamma_{sl}^{D^+}/\Gamma_{sl}^{D^0}$.
The total decay rates of the $D^0$ and $D^+$ mesons are underestimated in our
HQE approach and we suspect that this is due to missing higher-order QCD
corrections to the free charm quark decay and the Pauli interference
contribution. For the $SU(3)_F$ breaking ratios $\tau (D_s^+) / \tau (D^0) $
and $\Gamma_{sl}^{D_s^+}/\Gamma_{sl}^{D^0} $ our predictions lie closer to one
than experiment. This might originate from the poor knowledge of the
non-perturbative parameters $\mu_G^2$, $\mu_\pi^2$ and $\rho_D^3$ in the $D^0$
and $D_s^+$ systems. These parameters could be determined by experimental
studies of the moments of inclusive semileptonic $D$ meson decays.
