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Why is there no form of “do” in questions of the type “who knows?”
I want to know which is the correct way to ask this question:
Who wrote this song?
or
Who did write this song?
If the first one is the correct one, why doesn't it have an auxiliary? Which rule does it follow?
You only need "do" support when there's inversion. So if the WH-word/phrase is the subject of the question (and so there's no inversion), then you don't need "do":
What happened?
Which computer calculates faster?
On the other hand, if the WH phrase is the object (and there is inversion) then you need "do":
What did you drink with your meal?
Which computer did you buy?
Alternatively, if there's already an auxiliary verb (including a modal), you don't need add another one with inversion (and indeed, inversion or not, you can't usually use "do" alongside another modal/auxiliary):
Which computer can I buy?
When will you finish by?
An exception that can occur, in questions just like in ordinary statements, is that the auxiliary "do" can be used to mark a contrast. For example:
Speaker A: Mr Scarface didn't steal the car.
Speaker B: Well who did steal the car, then?
Another exception is so-called in situ questions, where you ask a question for confirmation/out of surprise, and where there's no inversion even though ordinarily there would have been. In this case, again because there's no inversion, you don't use do support:
You bought which computer? (implies: "I'm surprised you bought that computer!", or "please confirm again which computer you bought because I didn't hear you properly")
Both are potentially correct, depending on context. The first is the simple past -- it's the most basic form of the past tense. "Wrote" is the past tense of "write." The second might be said in response to a negation, with emphasis on did:
"John didn't write this song."
"Who did write this song?"
Did can also be used in interrogative forms with more specific pronouns or nouns than "who." As in:
"Did Paul write this song? Or did you write it?"
