There are two very different questions here so let's break things down a bit
Why does sodium have an ionization energy?
Since electrons are negatively charged and nuclei (owing to the presence of protons) are positively charged, electrons will typically be drawn to the nucleus. The situation gets a bit more complicated by (a) the quantum nature of energy and (b) the presence of other electrons. Complication (a) is the reason why electrons do not behave like planets orbiting the sun because if they did the electron would eventually be pulled in to the nucleus. (More details probably requires a different question.) The second complication is more relevant to your question, because additional electrons will both repel the electron we are trying to eject through ionization and also shield some of the positive charge of the nucleus. (Think about wearing sunglasses; they don't make the sun less bright, they just make less light reach your eyes.)
Your comparison of Na to that of an object on a cliff is not correct; the sunglasses analogy I used above is better (although it's flawed as well). The reason why sodium, or any other atom/ion for that matter, has an ionization energy is because it requires energy to separate two oppositely charged particles. The attraction may be weak, as it is in sodium, but it is still non-zero.
Why does $\ce{FeCl3}$ bond the way it does?
First, it is a good idea to look at the wikipedia page for iron(III) chloride, which shows that the molecule actually binds in an octahedral fashion, where two additional chlorides from neighboring molecules bind in a bridging fashion. This is a type of bonding that is typically not discussed until one's third year of chemistry education. Valence shell electron counting works really well for identifying "stable" electron configurations of ions and covalent molecules made out of lighter elements (C, N, O, for example). The presence of d-orbitals, plus the ionic nature of the interaction between Fe(III) and chloride ions, plus the Lewis acid/base concepts that do a better job at describing and rationalizing bonding in transition metal complexes, makes the concept of valence electrons not the best model to explain bonding in $\ce{FeCl3}$.
Without access to molecular orbital theory, it is perhaps best to explain the bonding in iron(III) chloride from a strictly ionic bond nature. Fe(III) is a +3 cation and therefore requires three -1 anions to balance the charge.