To what extent is the hadith "A menstruating woman should not recite anything from the Qur’an" authentic, and based on it, is it permissible for a menstruating woman to repeat the Qur’an along with a cassette tape?

The correct view is that it is permissible for a menstruating woman to recite the Quran from memory. The evidence for this is what was narrated from 'Aisha, may Allah be pleased with her, that the Messenger of Allah, peace and blessings be upon him, said to her: "Perform all the rituals of Hajj that a pilgrim performs, except for circumambulating the Kaaba, until you become pure." It is known that a pilgrim recites the Quran. As for the hadiths that prohibit this, they are weak. However, it is not permissible for a menstruating woman to touch the Mushaf (definition) (the physical copy of the Quran), due to the words of Allah the Almighty: "None touch it except the purified." [Al-Waqi'ah:79]. Rather, she should recite it from memory or by repeating it verbally.