Personally, I prefer function over form, but if I can have both, I'm not going to argue. Fire is as innate to me as my voice is, so most of my spells do indeed take that form.

As for the other women, there are a good number of fighters, mostly swordswomen of various types for some reason. However, there's a whole social cross-section of women here, from simple students to scientists to royalty. Age is also highly varied, from 9 or 10 to "immortal and age-irrelevant".