This question requires evaluating the correctness of statements related to fundamental network theorems: Superposition, Thévenin's, and Norton's theorems.

Analyzing Network Theorem Statements

Statement 1: Superposition Theorem Applicability

• The Superposition Theorem states that in a linear network containing multiple independent sources, the response (voltage or current) in any branch is the algebraic sum of responses caused by each independent source acting alone.
• To apply this theorem, independent sources are deactivated one by one (voltage sources replaced by short circuits, current sources by open circuits).
• Dependent sources are not deactivated; they remain active and are controlled by their respective variables in the circuit.
• The statement mentions "control functions are external" and "controls are unchanged". This is inaccurate. Control variables for dependent sources can be internal to the network, and they change as independent sources are activated individually. The linearity of the network is the primary condition.
• Therefore, Statement 1 is incorrect.

Statement 2: Thévenin and Norton Equivalents

• Thévenin's Theorem allows any linear, two-terminal network to be replaced by an equivalent circuit consisting of a single voltage source ($V_{Th}$) in series with an equivalent resistance ($R_{Th}$).
• Norton's Theorem allows the same network to be replaced by an equivalent circuit consisting of a single current source ($I_N$) in parallel with an equivalent resistance ($R_N$).
• $V_{Th}$ is the open-circuit voltage across the terminals, and $I_N$ is the short-circuit current across the terminals.
• Statement 2 accurately describes these equivalents for a linear, active, resistive network.
• Therefore, Statement 2 is correct.

Statement 3: Equivalent Resistances in Thévenin's and Norton's Theorems

• The equivalent resistance ($R_{Th}$ or $R_N$) in both Thévenin's and Norton's theorems is calculated by deactivating all independent sources within the network.
• Voltage sources are replaced by short circuits ($0$ V).
• Current sources are replaced by open circuits ( $0$ A).
• The resistance is then measured across the terminals of the network.
• This calculated resistance is the same for both $R_{Th}$ and $R_N$.
• Therefore, Statement 3 is correct.

Conclusion

Based on the analysis, statements 2 and 3 are correct, while statement 1 is incorrect.