The question is fine.
The response is not. The point about the question is that it is not really a question demanding an answer. It is something said as a sign of indignation.
Yes
I don't know what you mean by 'instigate'.No.
With the quotation marks, you have to quote what Tom said: Tom said to her, "How dare you touch my car?"
As reported speech, write: Tom asked her how she dared to touch his car.
Neither of these is particularly natural.
It's used in BrE, but it would come after the person said the thing that was causing offence, not before it.
No. I believe Tdol was referring to "how dare you?"
Where did you learn "instigate"? Do you remember?
I heard someone say it years ago.
Is it regarding instigate?
No, because the sentence you use it in doesn't work with any definition of the word.
I don't see that How dare you say such a thing to me!, when said in anger, is a question at all, and I wouldn't want to transcribe it with a question mark. And since it's not a question, it doesn't elicit an answer.
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