It's natural to shift tenses or aspects in casual speech. Compare with English: - You will go to Canada to deal with this. - OK. When am I going?
It seems that (at least in your examples) if a person asks for something the perfective is preferable
(sounds natural in orders or requests, please do it, сделай..., etc.), but the person answering is thinking about the process, how they are going to do it - so from their point of view the imperfective may often fit better (что делать? как делать? etc.).
Besides in your examples the second person doesn't really answer. They comment on the situation and are free to choose imperfective, as they continue the dialogue in a natural way.
NOTE: что, где, когда are irrelevant here. So your question might look better if you just ask WHY imperfective is used in the answer/comment, when perfective is used in the question/starting remark.
When am I going?a party conveys their agreement, compliance. Saying like that the process is already going they signal that the decision is made that it is final, and while the physical movement may not started yet, the very process in a broader sense is already going. – Arioch Apr 23 '19 at 16:51