Step 1: Write the reaction of $NaBH_4$ with iodine.
Sodium borohydride reacts with iodine to give a salt and two gases: \[ 2NaBH_4 + I_2 \rightarrow 2NaI + B_2H_6 + H_2 \] So the salt is $NaI$, and the two gases are diborane and hydrogen.
Step 2: Name the two gases Y and Z.
Diborane $B_2H_6$ is toxic, so it is the toxic gas Y. Hydrogen $H_2$ is combustible, so it is the burnable gas Z.
Step 3: Check statement I about Y with NaH.
Diborane reacts with sodium hydride to form sodium borohydride again, which is a well-known good reducing agent. So statement I is correct.
Step 4: Check statement II about hydrolysis of Y.
When diborane is hydrolysed, it gives boric acid. Boric acid behaves as a weak monobasic acid in water. So statement II is correct.
Step 5: Check statement III about Z.
Hydrogen gas is used in the Haber process to make ammonia from nitrogen. So statement III is correct.
Step 6: Combine the verdicts.
Since statements I, II, and III are all correct, the right option lists all three.
\[ \boxed{\text{I, II, III}} \]