Is it permissible for a husband and wife to live separately to avoid divorce, with the husband visiting his wife in her separate dwelling? And is it permissible for the wife to remove her niqab due to the department she studies in prohibiting it, even though she dislikes it and it causes problems with her husband?

The questioner is advised to strive to reform his wife and bring her back to righteousness and kind companionship, by encouraging her to associate with righteous women, listen to admonitions, and learn religious rulings, using wisdom and gentleness, and seeking Allah's help. If she becomes righteous, then that is good and blessed. If that does not benefit, and you see fit to allow your wife to live separately to avoid divorce, there is no harm, provided you place her in a safe place for her and her daughter. This opportunity should be used for reflection and consideration of the marital relationship.

Regarding the niqab, our fatwa is that it is obligatory. Therefore, it is not permissible for your wife to remove it merely because her workplace prevents her from wearing it or because she dislikes it. She should seek another job free from religious prohibitions, and if she does not find one, she should not continue in her current workplace unless there is a necessity for work. In that case, she should fear Allah as much as she can, cover her face outside of work, and uncover it at work only as needed.