1. He like talking with the native speaker in the teacher's room.
2. He likes talking with the native speaker in the teachers' room.
(Which one is correct, 'teacher's' or 'teachers''?)
Number 2 is correct because teachers' is the plural possessive. The teachers' room belongs to all of the teachers.
Of course, this could mean the classroom of one particular teacher - in which case it would be teacher's room (singular possessive).