I think the book deliberately leaves it open whether an Archmage is even being sought - 'A Woman on Gont' is the answer to a question the council of Roke haven't necessarily properly stated yet. Maybe she's to be Archmage, but maybe it's something else.

For the rest - I think other replies cover my feelings!

It was a good film wasn't it! (Night Train to Munich). I keep thinking: golf clubs! How long will they be telling that story?