Assalamu alaykum. Is it permissible to work in a website as writer and in this website you are gonna find people who need writers but in this website they are displaying woman in their website with no headscarf so is that permissible? and also is it permissible to learn courses where woman is display on website? and is it permissible to have a female teacher in school or at online?

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.

To answer your first question, if the website does not exclusively or prevalently publish forbidden matters, as in the case of the pornographic websites, but some images of women only appear on it, then there is apparently no reason to prohibit working as a writer for it, and permissible forms of participation with these kinds of websites is not considered as cooperation in what is forbidden, although it is still obligatory not to look at the forbidden images, or to conceal them. This is because such images have become a general problem and it is difficult to completely avoid them. A general rule from the Sharee‘ah is that if the case becomes narrow it expands (i.e. if a matter is difficult, concessions are given options), as Imaam Ash-Shaafi’i and others have stated. As-Suyooti quoted him as saying this in his Al-Ashbaah wan-Nathaa’ir.

Moreover, the images are not themselves the object of intent, and some matters are overlooked if they are dependent on something else, even if what they depend on is not overlooked, and some things are valid as depending on something else even if they are not valid independently,  and a dependent matter is not independently judged as long as it is not the object of intent, as stated in Az-Zarqa's commentary on Al-Qawaa'id Al-Fiqhiyya. As-Suyooti also said in his Al-Ashbaah wan-Nathaa'ir that some matters are overlooked inclusively even if they are not overlooked intentionally.

As regards the second question, it is permissible to join and participate in courses provided that one does not look at forbidden images when they appear, because it is not permissible to look at forbidden images to learn, and one must lower his gaze when they appear and not continue to look at them.

Concerning the third question, the Sharee‘ah commands us to separate between men and non-Mahram women, and to block the means that lead to men being tempted by women and women by men. So, as a rule, men should teach men and women should teach women, in order to be on the safe side. This is also more in line with the objectives of the Sharee‘ah. But if a man taught women or a woman men, it would be permissible provided that it was free of matters that contravene the Sharee‘ah, such as women not wearing Hijab, women speaking in an attractive voice, forbidden looking, forbidden mixing and so forth.

For more benefit, please refer to Fataawa 115043and 269953.

Allaah Knows best.