Regarding the housework for the wife there appear to be difference of opinion.

Answer

Yes, it is morally incumbent on her. It is the duty of the wife to do the housework. The husband is required to engage a maid to assist his wife with the housework. Rasulullah (sallallahu alayhi wasallam) very clearly stated that the housework is the obligation of Hadhrat Faatimah (radhiyallahu anha) and the outside work (of earning, etc.) is the duty of Hadhrat Ali (radhiyallahu anhu).

Even the Hanafi Fuqaha who say that housework is not Waajib on the wife, do not negate the wujoob (compulsion) of obedience to the husband in all things lawful. Thus, while cooking according to some is not Waajib on the wife by virtue of the Nikah, it becomes Waajib on her by virtue of the husband's instruction. It is another issue if the husband oppresses her with burdens, for then he is guilty of sinning, but his sin does not justify the wife's disobedience, hence Rasulullah (sallallahu alayhi wasallam) said that if the husband orders his wife to stand the whole night or to transfer the stones of one mountain to another, then she has to obey. The emphasis is on obedience of the wife to her husband in all things lawful.

According to the other Math-habs, housework is Waajib on the wife by virtue of the Nikah contract, not by virtue of the husband's orders. Rasulullah (sallallahu alayhi wasallam) has instructed his beloved daughter, Faatimah (radhiyallahu anha) to do the housework in her marital home, and this Hadith is the basis for the view of the other Math-habs as well as for many Hanafi Fuqaha.