Redox Combustion Reactions
Your redox equations look awkward (and wrong, too) because you are trying apply the half-reactions method as if it  were happening in aquatic media to the combustion reaction, which effectively occurs in the gas phase.
Of course, there should be no requirements for water to be present.
As it's been noted in the comments, ionic half-reactions method is not the most elegant way of find coefficients in this case.

If you really want to use it, I'd suggest to write the elements undergoing redox reactions separately from the corresponding compounds (and yes, we do consider oxygen being reduced into carbon dioxide too):

$$
\begin{align}
\ce{2 \overset{-3}{C} &amp;→ 2 \overset{+4}{C} + 14 e-} &amp;|\cdot 2 \tag{ox} \\
\ce{\overset{0}{O}_2 + 4 e- &amp;→ 2 \overset{-2}{O}} &amp;|\cdot 7 \tag{red} \\
\hline
\ce{4 \overset{-3}{C} + 7 \overset{0}{O}_2 &amp;→ 4 \overset{+4}{C} + 14 \overset{-2}{O}}
\end{align}
$$

resulting in a balanced equation:

$$\ce{2 C2H6 + 7 O2 → 4 CO2 + 6 H2O}$$

Note that in general there is an average oxidation number of carbon involved, and it might as well be fractional.