Is informing two out of three committee members about erroneous results in the research program submitted by the student sufficient to clear him of the accusation of cheating, and are the certificate and the money earned thereby considered unlawful, bearing in mind that the supervising professor ordered him to present only the correct results?

You must resist the whisperings (waswas) that led you to abandon prayer, by turning away from them and remembering Allah the Almighty. You can also seek specialized medical treatment. There is no cheating in the final results if the problem lies within the program, and your innocence is confirmed by presenting the problem to another trustworthy professor. Even if we assume there was previous cheating, there is no harm in you continuing your job and salary if you succeeded in it, and you still owe repentance for the cheating, which is what scholars like Sheikh Ibn Baz have ruled.