What is meant by a chemical equation? What do the symbols g, l, aq and $\rightleftharpoons$signify in the following equation?

${\mathrm{CO}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\rightleftharpoons {\mathrm{H}}_2{\mathrm{CO}}_3\left(\mathrm{aq}\right)$

By passing electric current through water, ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ are obtained as: 

$2{\mathrm{H}}_2\mathrm{O}\stackrel{\mathrm{electric} \mathrm{current}}{\to }2{\mathrm{H}}_2+{\mathrm{O}}_2$

But ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ can also be combined to form water

$2{\mathrm{H}}_2+{\mathrm{O}}_2\to 2{\mathrm{H}}_2\mathrm{O}$

The first reaction is a decomposition reaction and the second reaction is a combination reaction. Is this statement true? Justify.

Classify the following reaction as combination, decomposition or displacement reaction:

${\mathrm{CH}}_4 \stackrel{\mathrm{catalyst}}{\to } \mathrm{C} +2{\mathrm{H}}_2$

Classify the following reaction as combination, decomposition or displacement reaction:

${\mathrm{SO}}_2 +{\mathrm{H}}_2\mathrm{O} \to {\mathrm{H}}_2{\mathrm{SO}}_3$