Which one of the following statements is correct for a reversible reaction? $A$ catalyst

For the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$,what is the relationship between $\Delta H$ and $\Delta E$?

Given the equilibrium constants for the following three reactions:
$(1) N_2 + 3H_2 \rightleftharpoons 2NH_3; K_1$
$(2) N_2 + O_2 \rightleftharpoons 2NO; K_2$
$(3) H_2 + \frac{1}{2}O_2 \rightleftharpoons H_2O; K_3$
The equilibrium constant for the reaction of $NH_3$ with oxygen to form $NO$ and $H_2O$ is:

The following lists contain reactions and their corresponding equilibrium constants at different temperatures:

List-$I$ (Reaction)	List-$II$ $(K_p)$
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ at $298 \ K$	$4.0 \times 10^{24}$
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ at $700 \ K$	$3.0 \times 10^{4}$
$N_2O_{4(g)} \rightleftharpoons 2 NO_{2(g)}$ at $298 \ K$	$0.98$
$N_2O_{4(g)} \rightleftharpoons 2 NO_{2(g)}$ at $500 \ K$	$1700$

If $\Delta H_1^0$ and $\Delta H_2^0$ are the standard enthalpies for the reactions $2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ and $N_2O_{4(g)} \rightleftharpoons 2 NO_{2(g)}$ respectively,then:

For the following reactions,which oxide is more stable?
$X_2 + O_2 \rightleftharpoons 2XO, K_1 = 5$
$X_2 + 2O_2 \rightleftharpoons 2XO_2, K_2 = 10$

At $500 \ K$,for a reversible reaction $A_{2(g)} + B_{2(g)} \rightleftharpoons 2 AB_{(g)}$ in a closed container,$K_C = 2 \times 10^{-5}$. In the presence of a catalyst,the equilibrium is attained $10$ times faster. The equilibrium constant $K_C$ in the presence of a catalyst at the same temperature is: