First, I'll answer your first question. There's no hard and set rule for how metals will act in biochemistry. They can act as Lewis acids to stabilize charges (e.g. enolase and terpene biosynthesis) or be directly involved in catalysis (e.g. prostaglandin synthase, zinc metalloprotease). So metals are actually much more interesting than organic compounds - they are very versatile, which makes them excellent catalysts. They can also just serve simple roles like binding oxygen in myoglobin and hemoglobin.
Second, Zn reactivity is not governed by its full d shell but rather how easily it loses electrons in its 4s shell. Note that this is beyond the scope of the MCAT and getting into organometallic chemistry but I figured that you might be interested in how it works. In general chemistry, you're taught to simply count the electrons in each orbital to figure out how many electrons an atom has in its outer shells. The problem with that is that while that method is excellent for explaining how isolated atoms behave, most atoms are bonded, either covalently or via coordination bonds, to something else. For Zn, it's very easy to lose the two electrons in the 4s orbital because when Zn coordinates ligands, it wants to use its s orbitals to do so to increase penetration to the nucleus and thus increase Coulombic stabilization. So you'll often see Zn in its +2 oxidation state. Organometallic chemists consider that to be a "d10" compound.
This is actually why Pd, Pt, Cu(I), and Ag(I) are generally unreactive. When they are coordinated to various ligands, their s electrons get "promoted" to the d shell so that neutral Pd is not actually a d8 compound but rather d10 and thus relatively inert.
