1. We evaluate each statement one by one.

2. Statement A: $E_{\text{cell}}$ is an intensive parameter.

• Cell potential does not depend on the amount of substance taken.
• Even if the size of the cell is increased, the emf remains the same.

Therefore, $E_{\text{cell}}$ is an intensive property.

So, A is correct.

3. Statement B: A negative $E^{\ominus}$ means that the redox couple is a stronger reducing agent than the $\mathrm{H^+/H_2}$ couple.

• Standard reduction potential is measured relative to the standard hydrogen electrode (SHE), for which $E^\ominus = 0$
• If a couple has negative standard reduction potential, it has less tendency to be reduced than hydrogen.
• Equivalently, its reduced form has greater tendency to get oxidized, so it behaves as a stronger reducing agent than $\mathrm{H_2}$.

So, B is correct.

4. Statement C: The amount of electricity required for oxidation or reduction depends on the stoichiometry of the electrode reaction.

• From Faraday’s law, $Q = nF$ where $n$ = moles of electrons involved.
• The number of electrons required depends directly on the balanced electrode reaction.
• Hence the electricity needed depends on the stoichiometric coefficients of electrons in the electrode process.

So, C is correct.

5. Statement D: The amount of chemical reaction which occurs at any electrode during electrolysis by a current is proportional to the quantity of electricity passed through the electrolyte.

• This is exactly Faraday’s first law of electrolysis.
• Mass deposited/liberated or amount of reaction is proportional to total charge passed: $Q = It$

So, D is correct.

6. Total number of correct statements

All four statements A, B, C, and D are correct.

Hence, the required integer is $\boxed{4}$

7. Comparison with stored correct answer

• Derived answer: $4$
• Stored correct answer: $4$

They match.