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

$8.8 \ g$ of monohydric alcohol added to ethyl magnesium iodide in ether liberates $2240 \ cm^3$ of ethane at $STP$. This monohydric alcohol when oxidized using pyridinium chlorochromate $(PCC)$,forms a carbonyl compound that answers the silver mirror test (Tollen's test). The monohydric alcohol is:

The reaction of allyl alcohol with $MCPBA$ ($meta$-chloroperbenzoic acid) is shown below:
Allyl alcohol $\xrightarrow{MCPBA}$ Product
What is the stereochemistry of the product of the above reaction?

Write the mechanism of the acid dehydration of ethanol to yield ethene.

Identify $Z$ in the reaction sequence: $CH_3CH_2CH_2Br$ $\xrightarrow{Aq. NaOH} X$ $\xrightarrow{Al_2O_3, \Delta} Y$ $\xrightarrow{Cl_2/H_2O} Z$

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