Central-Mosque.com article to write, work in progress.
Based on the explicit command in the Qur'aan, it is NOT permissable for a woman to display herself even in Hijab & Niqab for Dawah purpose unnecessarily.
يَـٰنِسَآءَ ٱلنَّبِىِّ لَسۡتُنَّ ڪَأَحَدٍ۬ مِّنَ ٱلنِّسَآءِۚ إِنِ ٱتَّقَيۡتُنَّ فَلَا تَخۡضَعۡنَ بِٱلۡقَوۡلِ فَيَطۡمَعَ ٱلَّذِى فِى قَلۡبِهِۦ مَرَضٌ۬ وَقُلۡنَ قَوۡلاً۬ مَّعۡرُوفً۬ا (٣٢) وَقَرۡنَ فِى بُيُوتِكُنَّ وَلَا تَبَرَّجۡنَ تَبَرُّجَ ٱلۡجَـٰهِلِيَّةِ ٱلۡأُولَىٰۖ وَأَقِمۡنَ ٱلصَّلَوٰةَ وَءَاتِينَ ٱلزَّڪَوٰةَ وَأَطِعۡنَ ٱللَّهَ وَرَسُولَهُۚ ۥۤ إِنَّمَا يُرِيدُ ٱللَّهُ لِيُذۡهِبَ عَنڪُمُ ٱلرِّجۡسَ أَهۡلَ ٱلۡبَيۡتِ وَيُطَهِّرَكُمۡ تَطۡهِيرً۬ا
[33:32] O wives of the prophet, you are not like any other women, if you observe taqwa (righteousness). So, do not be too soft in your speech, lest someone having disease in his heart should develop fancies (about you); and do speak with appropriate words. [33:33] Remain in your homes, and do not display (your) beauty as it used to be displayed in the days of earlier ignorance; and establish Salah, and pay Zakah, and obey Allah and His messenger. Allah only intends to keep (all sorts of) filth away from you, O members of the family (of the prophet), and to make you pure through a perfect purification.
Shaykh ‘Abd ar-Rahmaan ibn Naasir al-Barraak (may Allah preserve him) was asked: What is the ruling on a female daa‘iyah appearing on TV in full shar‘i hijab for the purpose of da‘wah and fatwas?
Praise be to Allah. To proceed:
The basic principle is that the woman is fitnah in her image and her voice. The Prophet (blessings and peace of Allah be upon him) said: “I am not leaving behind me any fitnah more harmful to men than women.” (Agreed upon). Hence those who follow their whims and desires are very keen to introduce women into all media programming, both audio and video. Based on that, it is not permissible for a woman to appear on TV, even if she is wearing hijab, in the name of da‘wah and giving fatwas, because innumerable men will listen to her even if she only appears on the channel on the basis of teaching women. Moreover, there is no need for her to undertake da‘wah and issue fatwas via TV channels. The basic principle is that that is to be done by men, and men are more suited to that. Throughout Islamic history men have been the ones to teach, call people to Islam and issue fatwas in the mosques and so on. They are the khateebs and imams. It is not permissible for women to do any of these things unless it is among other women.
Moreover it is well known that women’s participation in video and audio media results in things that are contrary to sharee‘ah, such as their going out unnecessarily, mixing with men, making images of them even if they do wear hijab. This results in negative consequences that Islam came to prevent, as Allah, may He be exalted, says (interpretation of the meaning):
“O wives of the Prophet! You are not like any other women. If you keep your duty (to Allah), then be not soft in speech, lest he in whose heart is a disease (of hypocrisy, or evil desire for adultery, etc.) should be moved with desire, but speak in an honourable manner.
And stay in your houses, and do not display yourselves like that of the times of ignorance”
A woman may be making a display of herself in her clothing even if she wears hijab.
Based on the above I say: It is not permissible for a woman to appear on satellite TV channels as a daa‘iyah, mufti or teacher. Rather she should restrict her da‘wah activities to her fellow women at home or in a school or in the women’s prayer space in the mosque.
On this occasion we advise our sisters who are in charge of Islamic channels to fear Allah and not to be deceived by the words of those who have wrong views and do not see anything wrong with women appearing on Islamic channels and even promote that and support it with specious arguments. It is sufficient to note that this is in accordance with the whims and desires of modernists, who do not care about anything but falsehood or that which leads to falsehood. Hence they like the Islamic channels on which women appear and they regard them as keeping pace with modern times, and they do not like the channels on which no women appear and they regard them as backward and describe the people in charge of them as being extremists. These people are like those of whom Allah, may He be exalted, says (interpretation of the meaning):
“but those who follow their lusts, wish that you (believers) should deviate tremendously away from the Right Path”
We ask Allah to guide us to the straight path and to keep us away from the path of those who earned His Anger and of those who went astray. End quote from Shabakat Noor al-Islam.
And Allah knows best.