is Reem a female name?
Yes, like the actress Reem Kherici
what is the difference between this word for teacher and mudaris?
Basicaly the same in meaning.
● Muallim معلّم comes from 3ilm عِلم "science" and it means therefore the one who gives you science and knowledge.
● Mudarris مُدرس comes from dars درس = course, it means the one who gives you the course.
In what situations would you use each one?
yup it is