Is it permissible to instruct a woman to recite the Two Testimonies (Shahadatayn) inside the mosque in the presence of male worshippers, and what is the ruling on the presence of non-Muslim women in the mosque in inappropriate clothing during days designated for introducing Islam?

It is permissible for a Muslim woman who has recently embraced Islam to enter the mosque to declare her conversion, especially in non-Muslim lands, as this provides reassurance for her and for the Muslims, provided that no harm or discord results from it and that she is modestly dressed.

As for inviting non-Muslim women to Islam, it is preferable that this be done by specialized female callers, or else from behind a screen, and that the gathering be separate (men and women each in their own space). It is preferable that the women's gathering be in a place other than the mosque if they are immodestly dressed; otherwise, it can be in the mosque, avoiding prayer times if possible, and providing them with dawah materials.