"What are God's 'female characteristics'?"
In Isaiah 66.12-13, it says, "For this is what the Lord says: 'I will extend peace to her like a river,
and the wealth of nations like a flooding stream;
you will nurse and be carried on her arm
and dandled on her knees. As a mother comforts her child,
so will I comfort you;
and you will be comforted over Jerusalem.' "
In Hosea 11.1-4, God says that Israel is like a son. "It was I who taught you to walk, taking them by the arms. ... I led them with cords of human kindness, with ties of love. To them I was like one who lifts a little child to the cheek, and I bent down to feed them."
Jesus, in Mt. 23.37, said, "Jerusalem, ... how often I have longed to gather your children together, as a hen gathers her chicks under her wings..."
Those are a few examples.
"Why does he tell women to submit to husbands?"
That's a much longer discussion, but in the same text (Eph. 5.21-33) he tells men and women to submit to each other, and while telling women to submit to men he tells men to self-sacrifice themselves for women to make women Godlike. The "submission" thing is hugely misunderstood. To take it as misogyny is a superficial reading that doesn't hold water with study.
"Since when is a child an extension of its mother's body but not its father's body?"
In the Mesopotamian mythology of Tiamat, she gives birth to several deities, is killed by Marduk, who splits her body in half, and the heavens and the earth are made out of her divided body (
http://en.wikipedia.org/wiki/Tiamat). That's why I said it's an extension of her body, not his.