Does a woman have to seek her husband’s permission to make up her missed days of Ramadan? Also, if a woman is fasting her missed days of Ramadan with the permission of her husband, but whilst in the middle of it her husband asks her to break the fast, what should be done?

Making up for missed days in Ramadan is as compulsory as Ramadan itself, therefore no permission should be sought in fulfilling a fardh obligation. However, as a matter of courtesy the husband can be informed of the days when the woman seeks to fast.

As for the second part of the question, if she is fulfilling a missed fardh fast then she is not allowed to break it.