Biochemical pathway approach:
Nitrification occurs in two enzymatic steps, both requiring molecular oxygen as the terminal electron acceptor, ammonia-oxidisers convert \( \text{NH}_4^+ \) to nitrite, and nitrite-oxidisers such as Nitrobacter, an obligate chemoautotroph, convert nitrite to \( \text{NO}_3^- \) using \( \text{O}_2 \) in their electron transport chain. Since Nitrobacter derives energy solely from this oxygen-dependent oxidation and cannot function anaerobically, both its obligate autotrophic aerobe classification and the dependency of nitrate formation on oxygen availability hold true, confirming that Statement I and Statement II are both correct.