All of these words are related but they are not synonyms and not really interchangeable. Like fault and mistake. A mistake is when you intend to do something correctly, but you mess up, it's a mistake. Or any error that occurred is also a mistake. But if you are the one who made the mistake, then we say it is your fault(the blame is on you). "It's my fault things turned out this way, I made a mistake". Guilt is an emotion, when you experience guilt we say you feel guilty. So you could say, "I feel guilty, because I made a mistake. It was my fault". Or, "I think he feels guilty because of the mistake he made. He blames himself." A wrongdoing is not exactly the same as a mistake or a fault. A wrongdoing could be a mistake, but mistake implies more of an accident, whereas wrongdoing implies intent. "The kid stole all the candy" is a wrongdoing, but "He messed up his presentation" is a mistake, not a wrongdoing. Wrongdoing usually implies something morally wrong was done. Hope this helps!

:-) additionally, you can be 'guilty' of something without feeling 'guilty' "He was found guilty of stealing" - he was found to have been responsible for the theft