Is an unmarried woman required to obtain her guardian's consent in all her affairs, and what should a married woman do if her husband approves of her work that is free of Sharia violations, while her guardian objects?

A girl is not required to seek her guardian's permission for every action, unless that action entails a danger. In such a case, she must seek permission. She may go out for da'wah (inviting to Islam), visiting relatives, and visiting the sick, provided she maintains modesty and chastity, and as long as her going out poses no danger. For a married woman, her affairs are with her husband. If he permits her to work in a place free of শরعي (Shari'ah) violations, then she may go out.