Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.
As to what follows:
With regards to answering your question we say, success is by Allah Almighty.
If a woman leads other women in prayer then she recites loudly where loud recitation is required because that is the characteristic of that prayer though it is not permissible if there are strange people around who are not mahrams (unmarriageable persons). This is the view held by the Shafites and Hanbalites. However the Malikites are of the opinion that she should not recite loudly but rather silently because loud recitation might lead to fitnah. This is also the view of the Hanafites but the correct view is the first one.
And Allah knows best
As for calling adhan, the majority of scholars from Hanafi, Maliki, Shafi and Hanbali schools of thought are of the opinion that it is not permissible because adhan was legislated for calling people for jama’ah (congregation) and women are not jama’ah. Furthermore, adhan requires that the voice should be raised and women are not capable of that.
The Shafites are of the view that it is desirable. Al-Nawawi said in Sharh al-Muhadhab (3/108):
“if we say she can call adhan then she should not raise her voice above what is heard by her companions. The Shafi scholars agreed on this in al-Umm. So if she raises her voice above that then it is prohibited as it is prohibited for her to uncover her face in the presence of men because they are attracted by her voice in the same manner that they are attracted by her face.”
And Allah knows best.
Dr. Khalid al-Muslih
14 / 06 / 1425 AH