Correct statement(s) about the compounds $\textbf{X}$, $\textbf{Y}$ and $\textbf{Z}$ is(are)

From the given reactions, we can identify the compounds $\textbf{X}$, $\textbf{Y}$, and $\textbf{Z}$ as follows:

Reaction 1: $\text{MnO}_2 + 4\text{HCl (conc.)} \rightarrow \text{MnCl}_2 + \text{Cl}_2 + 2\text{H}_2\text{O}$
The greenish-yellow gas $\textbf{X}$ is $\text{Cl}_2$.

Reaction 2: $\text{NH}_3 + 3\text{Cl}_2 \text{ (excess)} \rightarrow \text{NCl}_3 + 3\text{HCl}$
Compound $\textbf{Y}$ is $\text{NCl}_3$.

Reaction 3: $\text{Cl}_2 + 3\text{F}_2 \text{ (excess)} \xrightarrow{573\text{ K}} 2\text{ClF}_3$
Compound $\textbf{Z}$ is $\text{ClF}_3$.

Evaluating the given statements:
(A) $\text{Cl}_2$ is widely used as a disinfectant for sterilizing drinking water. This statement is correct.

(B) In $\text{NCl}_3$, the nitrogen atom is $sp^3$ hybridized and possesses one lone pair of electrons. This gives it a trigonal pyramidal structure, not a planar one. This statement is incorrect.

(C) $\text{ClF}_3$ is used in the enrichment of $^{235}\text{U}$ because it reacts with uranium to produce the volatile compound $\text{UF}_6$ ($\text{U} + 3\text{ClF}_3 \rightarrow \text{UF}_6 + 3\text{ClF}$). This statement is correct.

(D) $\text{NCl}_3$ is a weaker Lewis base than $\text{NH}_3$. The highly electronegative chlorine atoms withdraw electron density from the nitrogen atom via the -I effect, making the lone pair less available for donation compared to ammonia. This statement is incorrect.

Answer: $\textbf{X}$ is used for sterilizing drinking water.; $\textbf{Z}$ is used in the enrichment of $^{235}\text{U}$.