What is the ruling on women praying in mosques without seeing the imam or the rows of men, merely following along via microphone, and how does this differ from praying behind a radio, and what are the implications if women do not become aware of the imam's forgetfulness (suhooh)?

It is permissible for women to follow the Imam in the mosque, even if they do not see the Imam or the congregants, provided they are aware of his movements by hearing the takbeer, because the entire mosque is considered as one continuous space, and the continuity of rows is not a condition therein. This differs from following the Imam via radio, which is impermissible due to the lack of spatial connection between the rows.

As for the Imam's forgetfulness and women standing and sitting according to the original rule, whenever they realize that they have fallen behind the Imam and he has preceded them by one pillar, they must perform what they missed and then continue to follow the Imam. There is no blame on them for this, as it is a delay due to an excuse, and they are not required to perform the prostration of forgetfulness, because the Imam bears the forgetfulness of the ma'mum (follower).