What is the product of the mild oxidation of glycerol using $H_2O_2/FeSO_4$?

The enolic form of acetone contains

Product $(C)$ is

Consider the following reactions:
$(a)$ $CH_3-CH=CH_2 + HBr \rightarrow CH_3-CH(Br)-CH_3$
$(b)$ $CH_3-CH=CH_2 + HBr \xrightarrow{Peroxide} CH_3-CH_2-CH_2Br$
$(c)$ $CH_4 + Cl_2 \xrightarrow{hv} CH_3Cl + HCl$
Which of these reactions proceed via a free radical mechanism?

The product of the reaction shown is:

Compound $A$ $(C_{11}H_{14}O_4)$ is a degradation product of the antibiotic vermiculine. It undergoes the following reactions as shown in the image. Identify the unknown compound $C$ $(C_{11}H_{18}O_2)$.