A. $\mathrm{E_{\text {cell }}}$ is an intensive parameter.

This statement is correct. The standard cell potential ($\mathrm{E}^{\ominus}_{\text{cell}}$) is an intensive parameter because it depends only on the nature of the reactants and the products, and not on the size or shape of the electrodes or the amount of material present.

B. A negative $\mathrm{E}^{\ominus}$ means that the redox couple is a stronger reducing agent than the $\mathrm{H}^{+} / \mathrm{H}_{2}$ couple.

This statement is also correct. A negative standard reduction potential ($\mathrm{E}^{\ominus}$) for a redox couple indicates that the couple is a stronger reducing agent than the standard hydrogen electrode ($\mathrm{H}^{+} / \mathrm{H}_{2}$), which has a standard reduction potential of 0 V.

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

This statement is correct. The amount of electricity required for a particular oxidation or reduction reaction depends on the number of electrons involved in the reaction, which in turn depends on the stoichiometry of the electrode reaction.

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 statement is also correct. Faraday's laws of electrolysis state that the amount of chemical reaction at an electrode during electrolysis is directly proportional to the amount of electricity passed through the electrolyte.

Therefore, all of the statements A, B, C, and D are correct.