1. Statement I: H$_2$O is liquid at 25°C (boiling point 100°C) due to strong hydrogen bonding; H$_2$S is gas (boiling point -60°C) with weaker H-bonding, correct.
2. Statement II: H$_2$O is neutral (pH ~7); H$_2$S forms weak acid H$_2$S(aq) $\to$ H$^+$ + HS$^-$, slightly acidic, correct.
3. Both statements hold based on physical and chemical properties.
4. Thus, the answer is (1) Both statements I and II are correct.