When is it okay to use $Q=mc\Delta T$, is this equation only for calorimetry questions?
The equation $Q = mc \Delta T$ is appropriate for calorimetry at a constant volume. $Q$ here refers to the net heat transfer of the isolated system. Change in enthalpy, $\Delta H$, on the other hand, is really the total change in energy of the system, that is:

$$\Delta H = \Delta U + P\Delta V + V\Delta P$$

Where $P$ is pressure, $V$ is volume, and $U$ is the internal energy of the system, which is the sum of the system's net heat transfer ($Q$) and the work done on the system ($W$): $\Delta U = Q + W$. If we substitute the definition of $\Delta U$ into our equation for enthalpy, we get:

$$\Delta H = Q + W + P\Delta V + V\Delta P$$

Because any mechanical pressure-volume work performed on a closed system is equal to $-P\Delta V$, the equation further reduces to:

$$\Delta H = Q + V\Delta P$$

From this it becomes apparent that $Q$ and $\Delta H$ are only equal if pressure is constant (i.e., $\Delta P = 0$). The upshot of all this is that you should not assume $\Delta H$ and $Q$ are equal unless you're explicitly instructed to assume constant volume and pressure. When a problem refers to heat, it's almost certainly referring to heat transfer, $Q$, and not enthalpy change ($\Delta H$).