Am I sinful for not telling my friend how to purify himself from madhy after he asked me to keep quiet, and do I have to make him repeat his prayers if they were invalid?

Worry has taken hold of you. Therefore, you must turn away from these worries and pay them no mind. Do not speak with your friend about this matter, lest you cause him to fall into similar worries. Instead, advise him to consult scholars and read their writings. Avoiding whispers of doubt and turning away from them is their only cure. If you wish to clarify a religious ruling, state only what the scholars have said, warning against whispers of doubt, and avoid speech that might cause the person you are speaking with to fall into such whispers, until Allah grants you well-being.