Prayers and keeping fasts are forbidden during menses. Is reading of the Qur’ān also forbidden in that period? What if a person just recites certain sūrahs in his mind which he knows by-heart without touching the Qur’ān ? Is it forbidden to have sex during menses?

Reading the Qur’ān during this state whether by heart or through the Book is not forbidden by the Shari`ah.

Only sexual intercourse is forbidden during this period. Other forms of sexual interaction are allowed. The Qur’ān says:

They ask you concerning women's courses. Tell them: They are an impurity. So keep away from women in their courses and do not approach them until they are clean. But when they have purified themselves approach them in the manner the Almighty has directed you [in your instincts] -- for Allah loves those who constantly repent and keep themselves clean. (2:222)

Anas Ibn Mālik reports in the Sahīh of Imām Muslim:

Amongst the Jews, when a woman menstruated, they did not dine with her nor did they live with her in their houses. So the companions of the Prophet asked him and Allah revealed ... (See 2:222 above). The Prophet then said: You can do everything except having intercourse with her. (Kitābu’l Hayd)