Extreme value distributions

I'm currently reading up on extreme value theory and got stuck with the following problems/questions:

• Let's consider $X_i$ which consists of n independent normally distributed variables with zero mean and variance $\sigma_i^2$. As far as I understand, then the probability distribution of its maximum $F_{X_{max}}(y)=P(X_i shows a Gumbel distribution with $F_{X_{max}}(y)=exp(-exp(\alpha (y-u)))$. Is there any way to determine $\alpha$ and $u$ analytically?
• What is the effect of non-independency of the $X_i$ (in other words correlated variables)? Is there any well defined extreme value distribution resulting?

Thank you very much for you help (even references to corresponding papers/books)!

Best

Marc