What is the religious ruling on a wife helping her husband financially, how much should she contribute, and how much should she keep for herself?

The default rule is that a wife's money is her right, and it is not permissible for the husband to take it except with her permission. It is not permissible for the wife to work except with the husband's permission (unless she stipulated that before marriage), and the husband may stipulate a portion of her salary in exchange for his permission for her to work. It is not obligatory for a woman to help her husband with expenses, but it is a sign of good companionship and the best form of charity, and for it she receives two rewards: the reward for kinship and the reward for charity.