Must a husband financially compensate his first wife for cooking and laundry, given that he spends every night at her house and not at his second wife’s, knowing that the first wife objects to this arrangement?

You are not obligated to give your wife financial compensation for her domestic services, so long as women of her standing customarily perform such services for men of your standing. If you do so, it is a praiseworthy act of kindness. As for the justice that is obligatory between wives, it is in the equal division of time and overnight stays, unless a wife waives her right.