Is it permissible for a mother to install a surveillance camera and eavesdrop on her daughter, who resides in a student dormitory in another country, out of fear that she might fall into sin, especially given that the daughter is 20 years old?

A mother is not permitted to place a surveillance camera in her daughter's room, as this constitutes spying, which is forbidden. The correct way to protect a daughter is by raising her with faith and the awareness of God's omnipresence, and by encouraging her to adhere to her hijab and modesty, while also urging her to avoid situations that arouse suspicion and temptation.