Is the scholarship and salary permissible or impermissible, knowing that the reason for obtaining them was cheating on some sections of the high school exams upon which the scholarship was based?

If deception has occurred, then one must seek forgiveness and resolve not to return to it, and continue studying without paying attention to whispers (waswas) and delusions. Delusion does not affect the validity of one's studies, nor are rulings built upon it.