Is it permissible for a menstruating woman to enter the lower level of the mosque designated for laundries, magazines, classrooms, and the women's prayer area? And does the pillar that divides the row into two halves break the row?

If the lower floor is designated as part of the mosque, such that the people on both floors can hear the Imam's voice, then the prayer of everyone in it is valid. However, it is not permissible for a menstruating woman to sit in it because it is considered an extension of the mosque. Her passing through it for a need, however, is permissible.

If the endower did not intend for the lower floor to be a mosque, but rather a storage area, then it does not take the ruling of a mosque. It is permissible for a menstruating woman and someone in a state of major ritual impurity (junub) to sit in it. Prayer in it is permissible for those who cannot see the Imam or some of the congregants, and the ruling of their prayer in it is separate from the congregational prayer in the mosque. As for a pillar that interrupts the row, it does not harm the prayer, but it is preferable to avoid it.