The $S_{N}2$ reaction mechanism proceeds through ........

The major product $P$ of the above reaction is:

Hydrolysis of an alkyl bromide $X$ $(C_5H_{11}Br)$ follows first-order kinetics. Reaction of $X$ with $Mg$ in dry ether followed by treatment with $D_2O$ gives $Y$. What is $Y$?

Among the given halides,which one will give the same product in both $S_{N^1}$ and $S_{N^2}$ reactions?
$(I) \ CH_3-CH(CH_3)-CH_2-CH(Br)-CH_3$
$(II) \ \text{2-methylcyclohexyl chloride}$
$(III) \ \text{Chlorocyclohexane}$
$(IV) \ CH_3-CH(Br)-CH_2-CH_3$

Arrange the compounds of each set in order of reactivity towards $S_{N}2$ displacement:
$(i)$ $2-Bromo-2-methylbutane$,$1-Bromopentane$,$2-Bromopentane$
$(ii)$ $1-Bromo-3-methylbutane$,$2-Bromo-2-methylbutane$,$2-Bromo-3-methylbutane$
$(iii)$ $1-Bromobutane$,$1-Bromo-2,2-dimethylpropane$,$1-Bromo-2-methylbutane$,$1-Bromo-3-methylbutane$.

What is an alcoholic solution of $KOH$ used for?