Phenol at $25 \, ^\circ C$ is

Predict the major product for the following reaction:

Which of the following statements is not correct?

Phenol $(C_6H_6O)$ $\xrightarrow{Br_2 \text{ in } CS_2}$ $X$ (Major product)
Phenol $(C_6H_6O)$ $\xrightarrow{Br_2 \text{ in } H_2O}$ $Y$ (Major product)
What are $X$ and $Y$ in the above reaction respectively?

For phenol,which of the following statements is correct?

In which of the following reactions does carbon$-$carbon bond formation take place?