Can this construction also be used idiomatically as it can in English?
People might say in English:
and that response works fine. Would the same work in Swedish, as in:
Yup, it's used like that a lot.
For the question though, it would be more idiomatic to ask Varför då? (or Varför det?) than just Varför?. We tend to like to add the little då to one-word questions.
Could it also be "varför inte då?" Or does that work only if "varför" is alone?
The "tag då" is normally just attached to one-word phrases. Varför då? Vem då? När då? etc. In those cases, it's just there to fill out the phrase and doesn't change the meaning (or: it just makes it sound more normal), so we just skip it when translating into English.
If you attach då to a longer question, it changes the tone of the question. Often it becomes more impatient. This då can be translated into 'then' in English:
När då? = 'When?'
När kommer du då? 'When will you come then?' (or 'So when will you come?')
nej is only used as an interjection, never as a negation. In English of course no can be both.