How is the presence of $C_2H_5OH$ in $CH_3OH$ determined?

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:

The formation of diethyl ether from ethanol is based on:

The alcohol which reacts most easily with conc. $HCl$ is

With which of the following will $HBr$ react the fastest?

Consider the following reaction and identify the product $(P)$.