I) Decreasing the temperature would take away heat from the system (a product), driving the reaction towards the products. II) Evaporating product would take a product away from the system, driving the reaction towards the products. III) Adding a catalyst only affects the rate of the reaction and does not effect equilibrium.

According to Le Chatelier's principle, when you compress a system, its volume decreases, so partial pressure of the all the gases in the system increases. The system will act to try to decrease the pressure by decreasing the moles of gas. 

In an endothermic reaction, heat can be treated as a reactant. Thus, if you add more reactant (heat), the system will shift to get rid of the extra reactant and shift to the right to form more products.

In an exothermic reaction, heat can be treated as a product. Thus, if you add more product (heat), the reaction will shift to the left to form more reactants. 

By increasing the concentration of one of the reactants, the reaction will compensate by shifting to the right to increase production of products.

Increasing the concentration of one of the products (such as increasing [C]), however, would have the opposite effect. Increasing the temperature of an exothermic reaction would shift the reaction to the left, while increasing the temperature of an endothermic reaction would lead to a rightward shift. Finally, decreasing the volume leads to an increase in partial pressure of each gas, which the system compensates for by shifting to the side with fewer moles of gas. In this case, the right side has three moles of gas, while the left side has two; thus decreasing volume would shift equilibrium to the left.

Le Chatelier's principle states that changes in pressure are attributable to changes in volume. If we increase the volume, the reaction will shift toward the side that has more moles of gas. If we decrease the volume, the reaction will shift toward the side that has less moles of gas. Since the product side has only two moles of gas, compared to the reactant side with four moles, the reaction would shift toward the product side, and more NH₃ would form.

With increased pressure, each reaction will favor the side with the least amount of moles of gas. In this problem we are looking for the reactions that favor the products in this scenario. I will favor reactants, II will favor products, III will favor reactants.

An increase in volume will result in a decrease in pressure at constant temperature. As a result, the equilibrium will shift toward the side with the greater total moles of gas, according to Le Chatelier's Principle. This will result in less AX₅ being produced.

The K_eq tells us that the reaction favors the products because it is greater than 1. The definition of equilibrium is that the rate of formation of products equals the rate of formation of reactants.

Ksp is dependent only on the species itself and the temperature of the solution. Adding another compound or stressing the system will not affect Ksp.

Both Na₂SO₄ and ammonia are slightly basic compounds. Thus, adding ammonia will create a common ion effect, where less sodium sulfate will be able to dissolve and some would precipitate out of solution.