What is the ruling on the money of a teacher who feels he succeeded through bribery, even though he was unaware of it, and is it permissible for him to continue in his work, or should he leave it and give his money in charity?

You should not be overcome by the obsession of inability; rather, seek Allah's help and perfect your work. If you are unable to perform the educational mission proficiently, leave the job and look for what suits your abilities. The comparison of students should not be an obstacle, but rather an incentive for diligence and hard work. The salary is lawful, and its basis is the employment contract and your adherence to its terms.