Which of the following hydroxy ethers gives a $+ve$ test with Tollen's reagent?

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

Lucas test is used for the determination of

$HO-CH_2-CH_2-OH$ on heating with periodic acid gives:

$A$ toxic compound $A$ when reacted with $NaCN$ in aqueous acidic medium yields an edible cooking component and food preservative $B$. $B$ is converted to $C$ by diborane and can be used as an additive to petrol to reduce emission. $C$ upon reaction with oleum at $140^{\circ} C$ yields an inhalable anesthetic $D$. Identify $A, B, C$ and $D$,respectively.

Ethanol,when reacted with $PCl_5$,gives $A$,$POCl_3$,and $HCl$. $A$ reacts with silver nitrite $(AgNO_2)$ to form $B$ (major product) and $AgCl$. $A$ and $B$ are respectively: