1) In the eyes of God men and women are equal. However in terms of running a family there must be a balance and system of power so the family functions properly. Just as a government cannot have two presidents, a family cannot have two heads. The husband has specific duties and the wife has specific duties.
2) She controls matters of the house and the husband controls matters outside the house. This system creates a balance of power and a system that the marriage functions properly.
As for God, men and women are equal. Both have equal and same chance at attaining Gods satisfaction and entering into paradise.