Is it permissible to supplicate for marriage to a specific woman without her knowledge, and is it permissible to supplicate for any sister for success, guidance, and achievement in this world and in her studies, while believing that mixing is impermissible?

There is no objection to supplicating for marriage to a specific woman. It is permissible to supplicate for other believers, whether they are men or women, based on the Almighty's saying: "Our Lord, forgive us and our brethren who preceded us in faith," and the Prophet, peace and blessings be upon him, said: "Whoever supplicates for his brother in his absence, the angel assigned to him says: Amen, and likewise for you."