Enzyme-cofactor pairings:
$\text{Cu}^{2+}$: Essential cofactor in Cytochrome c oxidase (Complex IV) (III)
$\text{Zn}^{2+}$: Coordinated at the active site of Carbonic anhydrase (IV)
$\text{Mg}^{2+}$: Chelates ATP substrate in Hexokinase (I)
$\text{Se}$ (Selenium): Present as selenocysteine in Glutathione peroxidase (II).

Assertion (A) is true: lyases (EC class 4) catalyze the cleavage of C-C, C-O, C-N, and other bonds by elimination, leaving double bonds or adding groups to double bonds. Reason (R) is true: hydrolases (EC class 3) catalyze hydrolysis, transferring functional groups to water as an acceptor. However, (R) describes hydrolases and is not an explanation for lyase mechanism.

$K_m$ is the substrate concentration at which reaction rate is $\frac{V_{max}}{2}$ (B), hence its units are concentration (M, mM, $\mu$M) (A). It defines the hyperbolic relationship $V_0 = \frac{V_{max}[S]}{K_m + [S]}$ (C). Regulatory/allosteric enzymes show sigmoidal kinetics and do NOT follow standard Michaelis-Menten kinetics (D is false).