Why do reactions happen at all?
What makes some atoms/compounds reactive and some noble?


Unpaired electrons and how tightly these electrons are bound to their respective nuclei.


  Why do reactions happen at all? What is the fundamental truth behind a reaction? 




Because atoms are more stable together than they are apart, and systems will tend towards their lowest energy state.


  But why NaCl?


This is really a matter of ratios, which is the basis of chemistry. Different elements share their electrons in different ways under different circumstances. Some can donate their electrons ($\ce{Na}$, $\ce{Al}$, $\ce{Au}$), some accept electrons ($\ce{Cl}$, $\ce{O}$, $\ce{N}$), and others are somewhere in between ($\ce{C}$, etc.). Sodium and chlorine are very consistent with how they share electrons. Sodium has 1 valence electron, chlorine lacks 1 valence electron, and they combine in a one-to-one ratio. The formula unit of their salt is $\ce{NaCl}$.

When considering the salt of aluminum and chlorine, ask how many valence electrons does each atom have/need. I think you might begin to see the pattern.




$[1]$ Bond energy diagram