What is the maximum number of edges you can add to the wheel Wn and still obtain a planar graph?
I know that the outside of the wheel can always be a cycle of 3 and that W4 has max edges=6, W5=9, W6=12, and W7=15 edges... etc. So I know the pattern but I don't know how to put it into a formula for all Wn.
Maximal planar graphs $G$ have size $m=3n-6$, where $n=|V(G)|$. To get the maximum number of edges you can add to a wheel, keep in mind that the wheel on $n$ vertices $W_n$ has size $2(n-1)=2n-2$, so you should be able to add $(3n-6)-(2n-2)=n-4$ edges while preserving planarity. For example, $W_4$ is already maximal planar, and adding one more edge to $W_5$ to make it maximal planar.