Is a marriage concluded without a dowry (Mahr), deferred dowry, or a marriage-itemized list, and with the husband not performing the prayers (Salat), based on sound legitimate foundations, and does the wife have legitimate rights in the event of divorce?

Marriage without a specified Mahr (dower) is valid if its conditions are met (guardian, two witnesses). The wife is entitled to Mahr al-Mithl (a dower equivalent to that customarily given to women of her status) after consummation, and she has the right to waive it. In the event of divorce, she is entitled to the full Mahr al-Mithl after consummation. If divorced before consummation, she is entitled to mut'ah (a compensatory gift), and she retains all the rights of a divorced woman.