Nernst equation calculations
For (1), I think you made the mistake of using a different value for overall cell potential when you worked backwards. Because if you use the correct overall cell potential, you get $K = 31.52$, your $\log K$ would be different if you used $0.685$ (which would make $\log K = 69.43$). Using the correct $E_\mathrm{cell}$ will get you the correct value of $n$ that you're looking for.

To solve for (2), think of what $K$ stands for. It's the ratio of something. Rearrange the ratio to solve for the unknown. It might seem confusing since you might think of an electrochemical solution, but that isn't always the case.