I say, and with Allah's guidance: If the prayer area is not a mosque, then it does not take the ruling of a mosque, and it is permissible for the menstruating woman to enter and clean it. However, if the prayer area is a mosque with an imam and a muezzin, and the five daily prayers are established there, then it is not permissible for the menstruating woman to enter it. As for the bathrooms, there is no harm in cleaning them at all. And Allah knows best.