2) Can a menstruating woman recite the Quran?
The only verse that refers to the condition of a menstruating woman is the following:
22 – They ask you about menstruation. Say: “It is harmful. So keep away from women during menstruation, and do not approach them until they are relieved of it.”
2 The Cow, 222
As one can see this is the only sexual prohibition. God does not prevent a menstruating woman from reciting the Quran, performing her daily prayers or interrupting her fast. A menstruating woman may enter a mosque and perform her prayer. The woman has thus been kept away from God by the spokesmen of God for a length of time approximately equal to 1/6 of her lifetime.