What happens when an inert gas is added to an equilibrium system while keeping the volume unchanged?

For the chemical reaction: $BaO_{2(s)} \rightleftharpoons BaO_{(s)} + \frac{1}{2} O_{2(g)}$,$\Delta H = +ve$. At equilibrium,the pressure of $O_2$ depends upon:

Does the number of moles of reaction products increase,decrease,or remain the same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?
$(a) \quad PCl_{5(g)} \longleftrightarrow PCl_{3(g)} + Cl_{2(g)}$
$(b) \quad CaO_{(s)} + CO_{2(g)} \longleftrightarrow CaCO_{3(s)}$
$(c) \quad 3Fe_{(s)} + 4H_2O_{(g)} \longleftrightarrow Fe_3O_{4(s)} + 4H_{2(g)}$

In a reversible reaction,$K_c > K_p$ and $\Delta H = +40 \, kcal$. The formation of product will be less at:

Assertion : $A$ catalyst does not alter the equilibrium constant of a reaction.
Reason : The catalyst forms a complex with the reactants and provides an alternate path with lower energy of activation for the reaction; the forward and the backward reactions are affected to the same extent.

When $NaNO_3$ is heated in a closed vessel,$O_2$ is liberated and $NaNO_2$ is left behind. At equilibrium,