Jordi Gali Book First Edition Page 47 (need help for derivation)
This simplification of the infinite sum is commonly made by a differencing approach. You can see here an example of this approach in this kind of models.
Regarding with the assumptions mentioned by you, for $\hat{mc}_t$ since it's a deviation from the levels variable steady state, in the equilibrium there's no expectations and therefore $mc_t=mc\implies \hat{mc}_t=0$ for all $t$ in the steady state. In other words in the steady state the value of this variable is deterministic and zero, but by no means the short term expectancy of this value $E_t[\hat{mc}_{t+k}]$ has to be zero, nor this is the way the series is simplified.
With respect to $\pi_t$, something similar happens, since by definition $\pi_t=(1-\theta)(p_t^*-p_{t-1})$ (Galí, 2008, p.57) and again, in the steady state $p_t^*=p_{t-1}\implies \pi_t=0$, but as with the marginal cost there's not a reason why log-linearized inflation is expected to be zero, apart from being in the steady state.