Which of the following alkyl halides undergoes rearrangement in an $S_{N}1$ reaction?

Consider the following $E_1/S_N1$ reaction. The missing product$(s)$ is(are):

In the following reaction sequence,
$Br-CH_2-CH(Br)-Ph$ $\xrightarrow[2. NaNH_2]{1. Alc. KOH} X$ $\xrightarrow[4. Conc. HNO_3/H_2SO_4]{3. HgSO_4/dil. H_2SO_4, Heat} Y$
$X$ and $Y$ respectively are,

$C_3H_7I$ $(P)$ $\xrightarrow[\text{alc. } KOH]{\Delta}$ $Q$ $\xrightarrow{NBS}$ $R$ $\xrightarrow{KCN}$ $CH_2 = CH - CH_2 - CN$. $P$ can be:

What are $X$ and $Y$ respectively in the following reaction sequence?
$C_3H_6$ $\xrightarrow[\text{(C}_6\text{H}_5\text{CO)}_2\text{O}_2]{\text{HBr}} X$ $\xrightarrow{\text{Na/ dry ether}} Y$

The total number of monohalogenated organic products (including stereoisomers) formed in the following reaction is:
$A$ (simplest optically active alkene) $\xrightarrow[(ii) X_2/\Delta ]{(i) H_2/Ni/\Delta }$