Modal verbs
I've learned about modal verbs. So I can understand most of these things in sentences. But I've always confused about 'would' and 'would have + past participle'. For examples, like this sentences, "why would she lie?" or "Who would do that?". I don't get the nuance of this sentences. Why they put 'would' in this sentences? I think it could make sense without 'would' in first sentence, and use 'did' instead of 'would' in second sentence.

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I'm speaking from a standpoint of an English speaker rather than a language expert so experts can chime in.

As a teacher, when I am discussing certain behaviors with my students, I would say "why would you do something like that?"  In this context, I'm not really demanding an answer but making a point of explaining why certain behaviors are not acceptable.  So it is like a rhetorical question, a question that does not really require an answer.

But if I demand an answer immediately for something that they did , I would say:  "Why did you do that?" This time, the student has to give me answer because I am asking a question directly.