Does the marriage remain valid if the wife swears an oath by her husband's name not to wear makeup, then secretly wears it without his knowledge, and is it permissible for her to pay expiation without his knowledge?

If the husband swears an oath of divorce – whether he intends divorce or merely a threat – the divorce takes effect upon his breaking the oath. This is the view of the majority of scholars, which is the fatwa (definition) we follow, contrary to Ibn Taymiyyah, who holds that it entails expiation for an oath. If you do what your husband swore by divorce that you would not do, the divorce takes effect, and he may take you back if it is the first or second divorce.

However, if the husband swore by Allah that you would not wear makeup, then divorce does not take effect if you do so. Instead, expiation becomes obligatory upon the husband, and it is not permissible to pay the expiation on his behalf without his permission.