haha, I can see why you might think that, but I can assure you it's not.
I've finished school now, and won't be starting university for another couple of months (plus, it's the summer! ;)).
The Mathworld site provides a simple proof that if a complex function satisfies the Cauchy-Riemann equations, then it also satisfies the Laplace equation.
And it would appear that the reverse proof results in some additional constants -- so I think the answer to (2) will be a "no".
However, I do have a question about the derivation provided on the Mathworld page: it seems to make two assumptions:
i) That u+iv is second differentiable; and
ii) that D/(DxDy) = D/(DyDx) (D for Delta).
please come up with some of your thoughts!