When the question word (who) is the subject of the sentence, no auxiliary is used. An auxiliary is only used when the question word is the object. So it's: Who saw you? - 'who' is the subject Who did you see? - 'who' is the object

They are equally correct. Let's look at the difference between these two sentences: 1. Sally wrote the lyrics. 2. Sally did write the lyrics. They mean the same, however the second gives extra emphasis to the fact that Sally wrote the lyrics. #2 is like saying 2*." Yes indeed, it was Sally who wrote the lyrics." You would say #2, for example, in an argument with someone who claims that Sally did not write the lyrics. You would respond by saying "Yes, she did. Sally did write the lyrics". You would ask the question "Who did write the lyrics?" in a conversation with a friend like this: Friend: Bob didn't write the lyrics. Jane didn't write the lyrics. Paul didn't write the lyrics. You: OK then, but who did write the lyrics?

The second sentence is correct as long as the word "did" is emphasised. Imagine that there has been a misunderstanding about who wrote the lyrics for a song. For example... "We have just found out that John Smith didn't write the lyrics to the song." "Well, if it wasn't John Smith who wrote the lyrics, then who 𝒅𝒊𝒅 write the lyrics?" The word "did" is emphasised both verbally when being spoken, and when being written.