Step 1: Recall what governs $\text{S}_N1$ rate.
Only carbocation stability matters, tertiary is most stable, then secondary, then primary. Isobutyl iodide (1°) gives the least stable cation, sec-butyl iodide (2°) more stable, t-butyl bromide (3°) most stable, so the given order climbs exactly as expected, Statement I is fine.
Step 2: Recall what governs $\text{S}_N2$ rate instead.
Here it's about how open the backside approach is, more branching near the reacting carbon means more steric hindrance and a slower reaction.
Step 3: Apply that to the three bromides given.
n-Butyl bromide has the least hindrance (straight chain), isobutyl bromide has a branch one carbon removed, and sec-butyl bromide has the branch right at the reacting carbon, the most hindered of the three, so reactivity falls in exactly that order, Statement II checks out too.
Final answer: Option 1, Both I and II are correct.