Is it permissible for a wife to secretly take money from her well-off husband to meet her needs or to pay a fidyah that is due upon her, in the event that her husband does not give her any money?

If taking from the husband's money is limited to the obligatory expenses for food and clothing, then it is not theft but a right permitted by the Shariah, as stated in the hadith of Hind bint Utbah. However, if the taking is for anything else that the husband is not obliged to spend on, then it is a betrayal and a failure to safeguard the husband's money. It is forbidden to take from his money to pay a ransom unless with his permission.