Which of the following is called the Lucas reagent?

The product $(C)$ in the below mentioned reaction is:
$CH_3-CH_2-CH_2-Br$ $\xrightarrow[\Delta]{KOH_{(alc)}} A$ $\xrightarrow{HBr} B$ $\xrightarrow[KOH_{(aq)}]{\Delta} C$

What is the final product $(IV)$ in the following reaction sequence? $CH_3-CH(OH)-CH_3$ $\xrightarrow{PBr_3} I$ $\xrightarrow{Mg/ether} II$ $\xrightarrow{\text{Ethylene oxide}} III$ $\xrightarrow{H_2O} IV$

$CH_3-C(OH)(CH_3)-CH_3 \xrightarrow[cool]{Na_2Cr_2O_7} (P)$; Product $(P)$ in the reaction is

Identify the reagents $X, Y, Z$ for the following dehydration reactions of alcohols:
$CH_3-CH_2-OH \xrightarrow{X} CH_2=CH_2 + H_2O$
$CH_3-CH(OH)-CH_3 \xrightarrow{Y} CH_3-CH=CH_2 + H_2O$
$(CH_3)_3C-OH \xrightarrow{Z} (CH_3)_2C=CH_2 + H_2O$

Which of the following is not the product of dehydration of $1-$cyclohexylpropan$-1-$ol?