Why exactly does molten NaCl explode, when it is poured into water? Why does molten $\ce{NaCl}$ explode, when it is poured into water?
$\ce{NaCl}$ has a high melting point, $1074\ \mathrm{K}$ ($801~\mathrm{^\circ C}$). $\ce{NaCl}$ has a molar mass of $58.44\ \mathrm{g/mol}$, it has specific heat capacity of $36.79\ \mathrm{J/(K\cdot mol)} = 629.53\ \mathrm{J/(K \cdot kg)}$. therefore the $\ce{NaCl}$ at melting point temperature has $491,033\ \mathrm{kJ/kg}$ more thermal energy than $\ce{NaCl}$ in STP conditions ($1\ \mathrm{atm}, 20~\mathrm{^\circ C}$, temperature difference $= 780\ \mathrm{K}$)
According to one amateur video in youtube, the molten salt explodes when it is poured into water (c. 2:15)
What is the exact cause of the explosion?
The author of the video reasons that the phenomenon is purely physical and it is caused by that water heats up, vaporises and expands as a gas inside the glimp of very hot $\ce{NaCl}$ salt. But is it really everything that happens there?
Other possible processes present in such occasion are (this is just a list what comes into my mind):

rapid crystallisation of the $\ce{NaCl}$
chemical reaction between $\ce{Na}$ and water: $$\ce{2 Na (s) + 2 H2O (l) -&gt; 2 NaOH (aq) + H2 (g)}$$ (this causes explosion if $\ce{Na}$ is inserted into $\ce{H2O}$)
reaction between $\ce{Cl}$ and water: $$\ce{Cl2 + H2O -&gt; HOCl + HCl}$$
the rapid solubility of hot $\ce{NaCl}$ into water
thermal decomposition (thermolysis) of $\ce{H2O}$ into either monoatomic or diatomic hydrogen and oxygen, and reactions that follow this.

Also, the author fails to explain why no explosion occurs with sodium tetraborate nor sodium carbonate when each of them, in molten state, was poured into the water.
Understand that sodium chloride is not made up of sodium metal and chlorine gas but of sodium ions and chloride ions, held together by ionic interactions. Under these thermal conditions (liquefication), the compound will not decompose into its elements and therefore all reactions you suggested which include elemental chlorine or sodium cannot occur.

Dissolution of sodium chloride in water is neither strongly exothermic nor strongly endothermic, so any effects stemming from the dissolution are neglegible.

Also note that you neglected an important variable in your calculations. As far as I can tell, you only calculate how to arrive at melting-point hot solid sodium chloride. To liquefy, additional melting enthalpy has to be applied, a further reservoir of energy to draw from. This melting enthalpy is of course released upon rapid crystallisation, but you should really subsume it into the heat energy difference altogether.

Finally, thermal decomposition of water is not exactly a process that will happen quickly, as exemplified by (water) steam temperatures that can be huge. Check out this unrelated answer of mine about how much energy is required to heat water to $100~\mathrm{^\circ C}$ and boil it.

So all things considered: The principle contribution to the explosion is the rapid heating of water including boiling, leading to tightly compressed gaseous $\ce{H2O}$ which expands explosively. This concurs with the recrystallisation of $\ce{NaCl}$ which accounts for a non-neglegible portion of the energy added, but which is technically already present in molten $\ce{NaCl}$. All other processes are minor or impossible.