What is the ruling on interceding or making a recommendation in schools, such as someone recommending a student to a teacher? And is that considered an injustice to the rest of the students due to the teacher's attention to the recommended student and favoritism in grades?

If intercession leads to the neglect of other students, or to giving a student undeserved grades, then it is not permissible. However, if intercession is a means of ensuring a student receives their rightful due, then there is no harm in it. It may even be obligatory if it is the only way to ensure the deserving individual receives their right, such as when a teacher is unjust.