A catalyst has no effect on the relative stability of the reactants or products, nor does it effect the temperature of a reaction.

Instead, catalysts lower the energy of transition states, increasing their stability, to lower the overall activation energy of the reaction. When the reaction requires less energy, it proceeds at a faster rate.

All of the choices are true, except that catalysts can be in distinct phases than the reactants. These are known as heterogenous catalysts.

A catalyst is a substance that increases the rate of a reaction, typically by lowering the activation energy required to initiate a reaction. The catalyst does not affect the equilibrium of a reaction, and is not consumed during the reaction.

Catalysts are substances that increase reaction rates without being consumed in the reaction. They decrease the activation energy needed, and they do not always need to be in the same phase as the reactants. In heterogeneous catalysis, the catalyst is in a different phase than the reactants. Equilibrium concentrations of both reactants and products are unchanged by the addition of a catalyst.

A catalyst will not be consumed during a reaction, so the catalyst will be whichever chemical is found both on the reactant side of the equation and on the product side.

For equation 1 that is compound Z; for equation 2 that is compound A.

Catalysts increase the reaction rate without being consumed during the reaction. They don't cause the reaction to make more product, but since the catalyst won't be used up in the reaction.

Enzymes function by forming complexes with their substrates at active sites. This interaction is often thought of as a lock and key mechanism, in the sense that the active site is shaped to fit a substrate. 

Enzymes are biological catalysts and therefore they work to lower the energy barrier or activation energy that prevents a reaction from proceeding to equilibrium. In other words: enzymes and catalysts in general make a reaction reach equilibrium faster.

Therefore enzymes do not change the equilibrium product concentration, just the time it takes to get to equilibrium.

Note that when catalyst decreases the activation energy (Ea),  will not be affected. The step in a reaction with the largest activation energy usually is the slow step, which catalysts facilitate. Catalysts do not affect the thermodynamic quantities . Since catalysts are not consumed in the reaction, they do not appear in the net equation of the reaction.

Using the equation , n being the number of moles, R being 8.314, and T being the temperature in Kelvin, we can find the kinetic energy of two moles of gas in a container.

The kinetic molecular theory of gases states that the average kinetic energy of gas particles is proportional to temperature, and it is the same for all gases at a given temperature. This is the opposite of what is stated in the answer choice.