Synthesis of glycerol from methane?
Your synthesis is unlikely to become a huge commercial success ;)

Methylchloride is a technical product, but usually made by reaction of methanol with hydrogen chloride:

$$\ce{CH3OH + HCl -&gt; CH3Cl + H2O}$$

This works nicely without side products, because


$\ce{CH3Cl}$ has a low solubility in water (around $\mathrm{5\,g\cdot L^{-1}}$)
under standard conditions, $\ce{CH3Cl}$ is a gas (bp around $\mathrm{-28\,°C}$)


The radical halogenation of methane will usually lead to various halogenation products and thus is not a good idea. The same is true for the similar reaction of ethane.

In addition, I fail to see how the reaction of ethanol and carbon dioxide will lead to glycerol.

You should further take into account that there's plenty of glycerol available as a side product in the production of biodiesel.

From a commercial and ecological point of view, methane therefore is better converted to cabon monoxide and hydrogen by steam reformation. Further hydrogen may be obtained from a subsequent shift reaction and the resulting carbon dioxide may be reacted with gycerol to yield 1,2-glycerol carbonate.