Did the niqabi woman commit a sin by removing her niqab for a photograph so that her sister could obtain a scholarship, and is an expiation (kaffarah) required of her for that?

There is no objection to a woman uncovering her face out of necessity, such as for a photograph that serves a preponderant interest. She does not incur sin by doing so; rather, the young woman is rewarded for assisting her family. If she intentionally uncovered her face where it is not permissible, she only needs to repent and seek forgiveness. She is not obligated to offer expiation through fasting or any other means. She should also strive to acquire knowledge of Islamic law.