Ladies performing Salaah in jamaat

Q: Please can you clarify for me. There is a masjid/classrooms/ladies namaaz area in one building. The masjid-mens namaaz area is on the first floor. The wuzu khanaa, classrooms and ladies namaaz area downstairs. The classrooms are used for namaaz when there is an overflow of males. The ladies area has a separate entrance door to that for the men and classrooms.

In some peoples mind, the ladies area does not form part of the masjid. They call it rooms. So they say, the ladies are not going to the masjid. Is this thinking correct? Can the ladies go to the masjid/rooms to make namaaz? Can the ladies read namaaz behind an Imam in Jamaat? Can the ladies go to the masjid/rooms to read namaaz but not in Jamaat? Can the ladies go to the masjid/rooms to read Taraweeh salaat in Jamaat? Can the ladies go to the masjid/rooms to listen to lectures? Can the ladies go to the masjid/rooms for a nikah? Can the Bride go to the masjid for her nikah but being in the ladies section? 

Are Ladies permitted to go to the masjid for any reason whatsoever?

Can the ladies go for Eid Namaaz to an Eid Ghah?

Please advise.

Q: We have a small Musallah at our University where five times daily salaat takes place. The Musallah is used by students and residents of the surrounding area. There is also a ladies Musallah. We have received a request from some of the residents of the area to allow ladies to follow the Imam in taraweeh salaah. The committee is unsure on the permissibility of this and would like to seek your advice. Another factor to take into consideration is that the only facility the could be available for ladies is a Wendy house that is situated alongside the males Musallah. (the ladies Musallah is in front of the Imam, hence ladies cannot follow from there). The wendy house is behind the Imam, but there is a gap between the males Musallah and the wendy house. The saffs do not flow from the males musallah into the wendy house. Will it be permissible to perform salaah in the wendy house?

Q: I know that it is necessary for the Imam to make in intention for leading the females in a congregation. However, what is the ruling if initially the congregation is all males, but then a female joins afterwards? Will the Imam have to change is intention in mid-prayer? Also, what if the imam never finds out that a female has joined the congregation (since he can't turn around), will the females prayer be valid?