What is the ruling on someone who felt wind exit after resisting it, then completed the prayer out of fear of intrusive thoughts (waswasah) and shyness from people, then repeated it later to remove doubt? And is his first or second prayer the accepted one?

A man does not need to repeat his prayer if his feeling of something having exited is merely a doubt, because the default state is the persistence of purity unless one is certain of its nullification. This is based on the Prophet's (peace be upon him) saying: "He should not leave (the prayer) until he hears a sound or perceives a smell." His first prayer is valid unless he is certain that his purity has been nullified.