What is the Michaelis constant (Km) in enzyme kinetics?

Given the Michaelis-Menten equation: v = (Vmax[S]) / (Km + [S]), rearrange it to solve for Km.

What does a small Km value indicate about the enzyme-substrate complex?

In a clinical setting, an enzyme with a small Km is observed. What might this suggest about the enzyme's role in metabolism?

If Vmax = 100 μM/s and v = 50 μM/s at [S] = 10 μM, what is Km?

If k-1 = 2 s^-1, k2 = 1 s^-1, and k1 = 1 s^-1, what is Km?

In a drug design scenario, why might a small Km be desirable for a therapeutic enzyme?