Is the presence of female Companions with men in the Messenger of Allah’s (peace be upon him) assembly considered unlawful mixing (اختلاط محرم)? What is the number by which mixing is achieved? And is it permissible for a veiled woman to mix with men?

The common mixing between men and women is forbidden. What the female Companions did by asking the Prophet, peace and blessings be upon him, is not considered mixing, because they were asking about rulings concerning their religion and they adhered to the hijab. This falls under the category of necessity. There is no specific number of men and women that permits mixing. It is not permissible for a woman to mix, even with a hijab; for the Prophet, peace and blessings be upon him, forbade entering upon women and being alone with them except in the presence of a mahram. If a woman is compelled to interact with men due to the necessity of work or treatment, and she adheres to the etiquette of Islamic law, then there is no sin upon her due to necessity.