How can a non-Muslim female teacher be invited to Islam, given the obstacle of not being proficient in the English language and the necessity of lowering the gaze, and how can her questions be answered regarding cutting off the hand of a thief, women's work, and the male's inheritance being twice that of the female?

The most important thing to focus on in Da'wah (inviting to Islam) is matters of faith. For when faith becomes firmly established in the heart, it becomes easy to accept the religious rulings. It is better for women to invite women to Islam, as this is safer. One can also seek assistance from some righteous young women who have a solid foundation in Islamic knowledge, or provide written and audio materials that introduce Islam, or guide her to Islamic websites that deal with introducing Islam.