Step 1: Analyzing Statement I
The correct entropy relation is:
\[
\Delta S_{\text{total}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}}
\]
Thus, the given equation is incorrect.
Step 2: Analyzing Statement II
When a liquid changes to a solid, the molecular disorder decreases, leading to a decrease in entropy. This statement is correct.
Step 3: Analyzing Statement III
The SI unit of entropy is \( J \ K^{-1} \) (not necessarily per mole). Thus, the given unit is misleading, making this statement incorrect.