By allowing the students to arrive at and leave the school at any time

A. of disciplining the students that will encourage them to be responsible and self-motivated and reduce the burden on the teachers who strive to concentrate on teaching rather than wasting
Parallelism error; teachers who strive to [concentrate on teaching rather than wasting]. "rather than" is our parallelism trigger and we have a two incorrectly parallel elements; infinitive (concentrate) and a gerund (wasting)

B. of disciplining the students that will be driven by responsibility and self-motivation and to reduce the burden on the teachers who strive to concentrate on teaching rather than to waste
First of all meaning is a little bit off; "a new way... that will be driven by responsibility and self motivation"? I think we can do better than that
Although parallelism may seem ok at first glance, it is not ok from a logical stand point;
Management intends to introduce....and to reduce... Management doesn't want to do two separate thing; what it really wants is to implement a new way through which students will gain responsibility/self-motivation and teachers will focus on teaching rather than wasting time on controlling the class

C. to discipline the students, while it will encourage them to be responsible and self-motivated and will reduce the burden on the teachers who strive to concentrate on teaching rather than waste
Illogical Meaning; "introduce a new way to discipline the students, while it will encourage them..." this basically tells that management wants to introduce a new way while this very new way encourages students. "While" implies a simultaneity so how is it possible for a "new way" that doesn't exist yet to affect the students?

D. of disciplining the students that will encourage them to be responsible and self-motivated and reduce the burden on the teachers who strive to concentrate on teaching rather than waste
Correct There is nested parallelism here; 1) that will [encourage...and reduce...] 2) teachers who [strive to concentrate...rather than waste...]

E. to discipline the students that will be driven by responsibility and self-motivation, while they will reduce the burden on the teachers who strive to concentrate on teaching rather than wasting
a new way that will be driven? neither does it sound extremely illogical nor extremely logical. Also same "while" error but this time it is worse, while students reduce burden? it is the new way that will reduce burden not students for sure