What is the ruling on benefiting from notes purchased by another person from a teacher I do not study with? And is it permissible for me to use notes that the teacher requested not be given to anyone?

What the sister bought in terms of notes and study guides, it is permissible to benefit from them. There is no significance to the teachers' prohibition of giving them to others, as long as they have sold them and received their price. So, she has the right to benefit from them and give them to whoever she wishes.