Assalaamu alaikum,
1. What is the ruling of Islam on women who work in public for religious or other activities.
2. Are women allowed to go to the Masjid to perform the Friday prayer and other prayers?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

In principle, a woman's work is restricted to her household duties, her familial duties and her maternal duties. She is not supposed to go out of her house except for a reason that is accepted under Sharee'ah, such as a personal or social need that requires her to go out of her house to satisfy that need, provided that the work does not include any violations to the Sharee’ah.

For example, it is lawful for a woman to work if she has no one to spend on her, and she must work in order to provide for her own living and expenses. Some women find themselves without means of support due to the lack or absence of family members, or due to them being poor, sick, or other reasons. In such cases, a woman is obliged to take care of herself within the limits set by the Sharee’ah.

Another example is when the society in need for her specialty such as in teaching fellow females, giving them medical treatment, calling them to Islam (Da'wah) and similar jobs which should be done mainly by women, because assiging such tasks to men would have more disadvantages than benefits. However, any work that a woman does should be compatible with her natur such as the administration of kindergartens, girls' schools, social foundations, charitable institutions designed for women and children and similar organizations provided it is free from any religious prohibition. However, if a woman is married, the permission of her husband is a pre-condition to any work that she does outside her home. Moreover, such work should not negatively affect the rights of her husband, children and her home as a whole.

Moreover, she must adhere to the proper Hijab, be decent, and avoid any place where she might mix with non-Mahram men or be alone with them. Besides, when going outside, a woman should not wear adornments or perfume as this is prohibited and could be reasons of temptation.

2  With regards to your second question, it is permissible for a woman to enter the mosque at any time provided that she is not in her menses, or in a state of sexual defilement or in Nifaas (the confinement period after childbirth). In such states, she should not enter the mosque until she becomes pure from any impurities. Allaah The Almighty Says (what means): {O you who have believed, do not approach prayer while you are intoxicated until you know what you are saying or in a state of Janaabah, except those passing through [a place of prayer], until you have washed [your whole body]. And if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and find no water, then seek clean earth and wipe over your faces and your hands [with it]. Indeed, Allaah is ever Pardoning and Forgiving.} [Quran 4: 43]

For example , the wives of the Prophet, sallallaahu ‘alayhi wa sallam, used to visit him while he,  sallallaahu ‘alayhi wa sallam, was performing I’tikaaf (confining oneself in the mosque with the intention of worship). It is also reported in an authentic narration that he, sallallaahu ‘alayhi wa sallam,  said: "The best rows for men are the first rows, and the worst rows for them are the last rows, and the best rows for women are the last rows and the worst rows for them are the first rows". The Prophet, sallallaahu ‘alayhi wa sallam, made it clear in this narration that women could join the congregational prayer in the mosque. Moreover, the Prophet, sallallaahu ‘alayhi wa sallam, ordered men not to prevent women from going to the mosque if they ask their permission to do so.

Allaah Knows best.