Is it permissible for a student to ask his teacher to leave the classroom after the lesson has ended but before the class period is over? And does the teacher have the right to expel him? And is my asking the teacher and acknowledging that there is no problem with my expulsion considered a mistake?

The teacher is not permitted to expel students from the classroom, even after the scheduled lesson has concluded, because the remaining time can be utilized for revision. However, we cannot say that he is never allowed to expel them under any circumstances or on any day. This matter refers back to the regulations issued by the competent authority. If you know that the teacher is not permitted to expel you, then it is not permissible for you to ask him to do so, as this would involve encouraging him to breach the trust placed in him.