Is it permissible for a woman who has been divorced three times to live with her ex-husband and their children (the youngest of whom is 16 years old) in the same house, provided she observes modesty and wears a hijab in front of him? And what is the ruling on serving him, preparing his food, and the permissible limits of speech?

If a woman is divorced with three pronouncements, she becomes a stranger to her husband, and the default is for her to reside far from him in a separate house. However, if there is an urgent need for her to remain in his house with her children, then a special place and private entrance must be designated for her, which the divorcing husband does not use. As for serving him and preparing his food, there is no harm in it if done in his absence without participation, and speaking with him should only be out of necessity, with modesty and dignity, and without being soft in speech.