In both scenarios, he has to leave the prayer immediately as his prayer became invalid, make wudhu and restart prayer from the beginning. This is the most authentic opinion of scholars. It is a major sin to continue praying though you know that your wudhu was broken, simply because you are ashamed from the people to know. The Prophet salla Allahu alaihi wa sallam directed to what to do by saying: If someone of you were to break his wudhu while praying, he should hold his nose and leave the congregation. Scholars said that he should hold his nose so that while going through the rows, people would think that his nose is bleeding.