Question 1: The mens masjid is opposite the womens musalla by a road approximately 12 metres wide.There is full speaker connection between the two buildings. Is the salah of the women accepted if they follow the Imam even if the mens hall is not completely full?Question 2.What if the distance of 12 metres gap is increased to 24 metres. Is the women's salah still valid in their premises even if the mens hall is not completely full?Question 3.The women's section has two halls seperated by approximately 20 metres. The back hall is reserved for women with children. Will the salah be valid in the back hall if the front sisters hall is not completely full?JazakAllahuKhairan we ask Allah to reward you. Please facilitate the allowing of this setup if there is room in the sharee'ah for it, because faculties are limited for women in this city. May Allah bless you.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

There is a difference of opinion among the scholars about all these different cases that you have mentioned in the question.

It appears to us that the prayer is valid if it is possible to completely follow the Imam through his sound even if it is through the loud speakers, and even if there is a road or a wall, and the like (between them). Ibn Qudaamah said:

“If there is a road between them, or river where the ships sail, or they were in two separate ships, then there are two views: The first view: is that it is not valid for the ones in one ship to follow in prayer those in the other ship, and this is the view chosen by our companions [i.e. the scholars of the Hanabli School], and it is also the view of Abu Haneefah. This is because the road is not a place for the prayer, so it resembles what prevents connection.

The second view: it is valid (to follow them in prayer), and in my view this is the correct opinion. This is also the view of Maalik and Ash-Shaafi'i. This is because there is no Islamic text that prevents from this (from being permissible), and there is no consensus on this issue, and this case is not similar to the scenario which they (the first group) prohibit, as it does not prevent them (one ship) from being led by the others in prayer. The factor which affects in this issue is something which prevents seeing them or hearing their voice; this case in not one of these two cases.” [End of quote]

The ruling becomes even more emphatic that being led by them in prayer is valid is when there is a need for this, Shaykh Ibn Taymiyyah said:

“If there is a barrier between them that prevents sight (seeing them) and prevents passing to the other side, then there are several views according to Ahmad and others. One view is that: it is permissible. A second view is that it is not permissible. A third view is that it is permissible in the mosque but not elsewhere. Yet, another view stipulates that it is permissible when there is a need but it is not permissible when there is no need. There is no doubt that this is absolutely permissible when there is a need, such as when the doors of the mosque are closed, or when the Maqsoorah is closed (Maqsoorah: a special place where the Imam and the state officials pray, and it is either an area on the same level surrounded with a fence or walls, or like a balcony which is also surrounded by a short wall). Here (in these cases) if seeing the Imam is obligatory, it is waived because of the need; as already discussed. We have already discussed that the obligations of the prayer and praying in congregation are waived if there is a valid excuse, and that praying in congregation is better than praying alone in all cases.” [End of quote]

In conclusion, the scenarios which the questioner mentioned are all valid, and women may follow [be led in prayer] the Imam as long as they are able to follow him through the sound.

Allah knows best.