The ruling on the mixing of men and women and what follows from it

Question:
Our brother asks another question, saying: The mixing of men and women, and men and women shaking hands with one another, when they are not mahram (relatives one may not marry), and you find a man sitting with his brother’s wife and shaking her hand. What is the ruling of Islam in this? And could this lead to very serious fitnah (trial, discord or temptation)? And what is the Islamic dress that a woman must wear?

Answer:
There is no doubt that the mixing of men and women in a manner that lacks modesty and lacks hijab (the covering prescribed for women) is among the greatest causes of fitnah (trial, discord or temptation), and this is not permissible. Rather, women must be covered, veiled, and kept away from the causes of fitnah (trial, discord or temptation) when they mix with men out of necessity, or to buy goods, or for the like of that. It is not permissible for her to be in seclusion with a man, such as her cousin, her husband’s brother, or her sister’s husband; it is not permissible for her to be in seclusion with him; because of the saying of the Prophet (peace and blessings be upon him): .
So it is obligatory for women to observe hijab (the covering prescribed for women), to be cautious of the causes of fitnah (trial, discord or temptation), and not to mix with men in a way that results in fitnah (trial, discord or temptation). A woman should not be in seclusion with a man, and she should not travel with him. All of this is among the causes of fitnah (trial, discord or temptation).
Likewise, regarding handshaking, she is not to shake hands with a man unless he is a mahram (a relative one may not marry) to her, such as her brother or her uncle; because handshaking also involves fitnah (trial, discord or temptation). So she is not to shake hands with a man unless he is a mahram (a relative one may not marry) to her, such as her uncle or her brother, or the like of that. And when there is a need to mix with men, she should be covered, veiled, and kept away from the causes of fitnah (trial, discord or temptation), until she gets what she needs from the market, and then she leaves.
Allah (Exalted and Majestic is He) says to the wives of His Prophet (peace and blessings be upon him): [Al-Ahzab: 33]. The meaning of "qarna" is: remain in your homes, meaning: stay in your homes except when going out is for a need and a benefit. Then He forbade them from tabarruj (a woman's display of her adornment), and He said: [Al-Ahzab: 33].
So tabarruj (a woman's display of her adornment) is displaying one’s beauties and charms. This is tabarruj (a woman's display of her adornment): displaying her beauties and charms among men, such as her face, or her hair, or her neck, or her hand and foot and chest. All of this is among the causes of fitnah (trial, discord or temptation).
It is obligatory for her to be covered, to wear the hijab, and to stay away from the causes of fitnah (trial, discord or temptation). Likewise, coquettishness in speech and submission in speech are prohibited; because of His saying (peace and blessings be upon him) in His great Book: [Al-Ahzab:32], meaning: the desire of the passion. So, submission in speech to men and softness are among the causes of fitnah. Rather, the voice must be moderate, without harshness and without submission, but an ordinary voice... with men. There is no harm in the voice with men; it is not an 'awrah (the part of the body that must be covered). The 'awrah is its submission, its coquettishness, and its breaking in tone, which may make men covet her. As for the ordinary voice, there is no blame in that. The women used to speak to the Prophet (peace and blessings be upon him), ask him, seek his fatwa (a scholarly legal ruling), and speak to the Companions (may Allah be pleased with them) . There is no harm in this. Yes.