Is it permissible to manufacture and sell open-toed shoes for women, and does the ruling differ if the seller knows that women in his country do not wear socks?

There is no objection to selling shoes to women, even if a woman exposes her feet when she goes out. This is because the merchant is selling something permissible that is used for a permissible purpose. This is not considered assisting in sin, because the sin (exposing the feet) has no relation to the shoe; rather, it is due to neglecting to wear something else, like socks. Furthermore, wearing shoes might mitigate the sin by covering part of the foot, and the seller is not obligated to monitor how women wear shoes. It is sufficient for him that he sells something permissible. Nevertheless, if it is possible to dispense with selling what is worn in a forbidden manner, that is better and more cautious.