This girlchild was born as usual and presented dolls that did pee-pee and miniature GE stoves and irons and wee lipsticks the color of cherry candy. (1-4)
We're guessing the speaker is referring to "usual" here as a way to describe the natural way every kid is born—nothing out of the ordinary there. And yet the pee-pee dolls and wee lipsticks are supposed to be "usual" too, even though it's not like kids come out demanding lipsticks or fire trucks.
Then in the magic of puberty, a classmate said: You have a great big nose and fat legs. (5-6)
Puberty is definitely not one of the finer moments of our coming of age experience. But it's necessary nonetheless and often becomes a period in which kids learn to mimic older folks pretty well. And as we see here, the act kids put on proves that adults may have some growing up to do too.
Her good nature wore out like a fan belt. So she cut off her nose and her legs and offered them up. (15-18)
In trying to please everyone else while growing up, the girlchild can't keep her natural engine alive, so to speak. So what's left to do? Offer up her nose and legs, the very things that everyone can't seem to stop fixating on.