Precipitation of CaCl2 and FeCl3 in Na2CO3
This must have been a very good question for a geochemist. They'd give you a complete answer with details of why $\ce{Fe2(CO3)3}$ does not but $\ce{Fe2O3}$ exist in our surrounding. Yet, I would like to give only a simple answer for the question: No, $\ce{Fe2(CO3)3}$ does not form (in sort) when you added $\ce{Na2(CO3)3}$ to an aqueous solution of $\ce{FeCl3}$. The reason?

An aqueous solution of $\ce{FeCl3}$ is acidic because $\ce{FeCl3}$ is a salt of a strong acid $(\ce{HCl})$ and a weak base $(\ce{Fe(OH)3})$. Thus an aqueous solution of $\ce{FeCl3}$ is in following equilibrium:
$$\ce {Fe^{3+} + 2H2O &lt;=&gt; [FeOH]^{2+} + H3O+ }$$
Thus, $\ce{H3O+}$ ions in solution can react with added $\ce{CO3^{2-}}$ ions to form carbonic acid $(\ce{H2(CO3)3})$,which can decomposed to form $\ce{CO2}$  and $\ce{H2O}$. Remaining $\ce{Fe^{3+}}$ will combine with left behind $\ce{OH-}$ ions to make $\ce{Fe(OH)3}$, which would decomposed to $\ce{Fe2O3}$. Thus, when $\ce{Na2CO3}$ is added to an aqueous solution of $\ce{FeCl3}$, one can expect the following sequence of reactions to be taken place: 
$$\ce {FeCl3 (aq) + Na2CO3 (aq) -&gt; [Fe2(CO3)]^{3+} (aq) -&gt; Fe2O3 (s) + CO2 (g) + H2O (l)}$$