Is it considered sufficient to inform two out of three members of an evaluation committee about a problem in the results of a research program to clear oneself of the guilt of fraud, and how can one get rid of the whispers of fraud that affect acts of worship?

We ask Allah for healing from obsessive thoughts. The cure for them is to completely ignore them and ask Allah for well-being, not by abandoning acts of worship or being negligent in prayer. As for whether your action constitutes cheating, it depends on the research system and the evaluation committee's assessment. If the committee members are authorized to approve the research despite its flaws, then it is not considered cheating. Even if the approval violates the system and you receive a grade you don't deserve, the entire degree is not invalidated, as the research is only one requirement and not the entirety of the study.