textbf{Step 1: Statement-1 analysis.}
Under certain conditions, oxygen exhibits a covalency of 4, such as in compounds like \( \text{OF}_2 \) and \( \text{SO}_2 \). In \( \text{SO}_2 \), the oxidation state of oxygen is \( -2 \), and in \( \text{OF}_2 \), the oxidation state of oxygen is \( +2 \). Hence, Statement-1 is correct. Step 2: Statement-2 analysis.
The anomalous behavior of oxygen in the 16th group, such as its ability to form compounds with oxidation states higher than \( -2 \) (like \( +2 \) in \( \text{OF}_2 \)), is indeed due to its small size and high electronegativity. Therefore, Statement-2 is also correct. \[ \boxed{\text{Statement-1 and statement-2 both are correct.}} \]