Is the reward earned from using educational materials (slides) belonging to the department for explaining to students outside official working hours permissible (halal), and is it permissible to purchase these slides with the approval of the officials?

If you are given full ownership of the means, then you may dispose of them as you wish. However, if they are given to you as a trust, or if custom dictates so, then you may not use them except with the permission of the one who holds authority. Otherwise, you must seek forgiveness or pay the equivalent rent.