Is it permissible for a woman to pray the funeral prayer, and was this mentioned in the Qur’an, and what should a woman do in this regard during Hajj?

There is no Quranic text indicating the funeral prayer (Salat al-Janazah); rather, it is established by the Sunnah of the Prophet. It is permissible for women to pray the funeral prayer, as there is no evidence prohibiting them from doing so. However, women participating in funeral processions is forbidden, as we have been prohibited from that, even if it was not an emphatic command. Al-Hafiz Ibn Hajar stated that the prohibition is one of discouragement (tanzih), not absolute prohibition (tahrim), and Malik inclined towards permissibility. Nevertheless, it is preferable for a woman not to go out to funeral processions, even if that means missing the funeral prayer, because her prayer at home is better, and she is commanded to observe modesty, and refraining from funeral processions is more appropriate for her.