How to determine the temperature dependence of equilibrium constants?
I agree that the second question seems a bit leading, but personally I would just calculate all quantities of interest as you laid on in your plan. The van't Hoff equation requires the reaction enthalpy change, so I assume using a tabulated value is fair game. If so, you will know whether the forward reaction is endo- or exothermic. If you calculate the equilibrium constant at the unknown temperature as you planned, you can compare it to the equilibrium constant given in the problem (for 727 C). Comparing these two equilibrium constants will tell you which way the reaction proceeded, and with the sign of the enthalpy, you should be able to deduce whether heat was added or lost... i.e. whether the new temperature is higher or lower than the initial state, 727 C (without having to go through the entire calculation).