Which functional group is present in the hydrocarbon chain of a detergent?

Explain the given reactions with examples:
$(a)$ Saponification reaction
$(b)$ Combustion reaction

$CH_{3}COOH + C_{2}H_{5}OH \xrightarrow[\Delta]{\text{conc. } H_{2}SO_{4}} (?)$

What is the role of the metal or reagents written on the arrows in the given chemical reactions?
$(a)$
$(b)$ $CH_{3}COOH + CH_{3}CH_{2}OH \xrightarrow{Conc. H_{2}SO_{4}} CH_{3}COOC_{2}H_{5} + H_{2}O$
$(c)$ $CH_{3}CH_{2}OH \xrightarrow[Heat]{Alkaline KMnO_{4}} CH_{3}COOH$

Identify and name the functional groups present in the following compounds.
$(a)$ $CH_3-CO-CH_2-CH_3$
$(b)$ $CH_3-CH_2-CH=CH_2$

What is the molecular formula of methanol?