Can I use sodium hydroxide (NaOH) to remove oxides from metals?
Your second reaction isn't a redox reaction. When carbon dioxide is dissolved in water, two equilibriums are forms:

\begin{eqnarray}
    \ce{H_2CO_3 + H_2O &amp;&lt;=&gt; HCO_3^- + H_3O^+} \\
    \ce{HCO_3^- + H_2O &amp;&lt;=&gt; CO_3^{2-} + H_3O^+}
  \end{eqnarray}

Remember that water also is in equilibrium:

$$\ce{2H_2O &lt;=&gt; OH^- + H_3O^+}$$

Adding $\ce{NaOH}$ will — according to Le Chatelier's principle, the equilibriums are disturbed, and more carbonate ($\ce{CO_3^{2-}}$) is formed.

If you're interested in a nice redox reaction involving iron(III) oxide, aluminium is much better choice.