Why I=(V(in)-V(out))/R in zener resistor circuit
The input to your "regulator circuit" is Vin - any problems with that?

The output from your regulator circuit is Vout (Vzener) - any problems here?

So, this MUST mean that the current thru the resistor is: -

\$ \dfrac{V_{IN} - V_{OUT}}{R}\$

It's ohms law - voltage across the resistor divided by its resistance equals current thru the resistor.

That is the current that always flows into the resistor from the input voltage. It will also be the current flowing into the zener when you have no load connected to Vout.