Is it permissible for a preparatory student to continue studying with a Christian female teacher after he saw her breastfeeding her son?

The basic principle is that it is permissible for a woman to teach adult males if she observes the hijab (definition) and there is no private seclusion (khalwa (definition)) or softening of speech. However, it is better for her not to teach them due to the potential for danger. It is not permissible for a young woman from whom temptation is feared to teach adult males unless there is a screen and no qualified male teachers are available. The situation mentioned in the question is not permissible under any circumstances, because the teacher is a non-Muslim, immodestly dressed, and breastfeeds in front of the students, while it is possible to find a competent male Muslim teacher. The student should refrain from going to this woman and seek a competent teacher.