How is the direction of a reaction predicted?

For ammonia formation from constituent elements,the expression for $K_{C}$ is

The value of $K_{c}$ for the reaction $3 O_{2(g)} \longleftrightarrow 2 O_{3(g)}$ is $2.0 \times 10^{-50}$ at $25^{\circ} C$. If the equilibrium concentration of $O_{2}$ in air at $25^{\circ} C$ is $1.6 \times 10^{-2} \, M$,what is the concentration of $O_{3} ?$

The equilibrium concentrations of $HI$,$I_2$,and $H_2$ are $0.7 \ M$,$0.1 \ M$,and $0.1 \ M$ respectively. The equilibrium constant for the reaction $I_2 + H_2 \rightleftharpoons 2HI$ is:

For the following three reactions $a, b$ and $c,$ equilibrium constants are given:
$(i)$ $CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)}$ ; $K_1$
$(ii)$ $CH_{4(g)} + H_2O_{(g)} \rightleftharpoons CO_{(g)} + 3H_{2(g)}$ ; $K_2$
$(iii)$ $CH_{4(g)} + 2H_2O_{(g)} \rightleftharpoons CO_{2(g)} + 4H_{2(g)}$ ; $K_3$
Which of the following relations is correct?

The equilibrium constant for the given reaction is $100$.
$N_{2(g)} + 2 O_{2(g)} \rightleftharpoons 2 NO_{2(g)}$
What is the equilibrium constant for the reaction given below?
$NO_{2(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + O_{2(g)}$