ANSWER: Making wudu while menstruating is not permissible.  You can recite surah kahf. No problem in reciting the Qur’an, doing dhikr, making adkhar for morning and evening etc during menses.  https://youtu.be/Nz2jk3aqvnY

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ANSWER: It is best to burn them if they are written in Arabic text. You can also shred or bury in a clean ground. 

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ANSWER: She does not have to be in the state of wudu in order to make sujood at tilawah. She can make the sujood while on her menses, though she can skip it altogether as it is not mandatory.

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