It's one of those examples wherein language is not a set of prescribed grammatically correct rules. Yes, formal rules of grammar incorporate past perfect, present perfect, and on and on it goes; in that regard, you are correct. But, colloquial usages mix and match words and bypass strict rules. Those who have mastered a language can play with the language. So . . . Yes, it's common to hear. Closer to home example: Person 1: "You finished?" Person 2: "Yep, all done!"

In "it's done" and "it's finished", the past participles are used as predicate adjectives; it's not the passive voice. We know this only by the context. In this situation, the passive voice would be "it's been done / finished", but that would imply that someone else did the work (or else we would just answer "yes, I have").

This is a great question. In the case of “it’s done”, I think done is acting as an adjective. We’re using the present to show it was done (ack) recently. I also agree with the person who said, when in doubt, you can answer using the same grammar as the question. https://www.oxfordlearnersdictionaries.com/definition/english/done_1

Hmm.. I would respond to 'Have you finished your work?' with 'Yeah, I have' or 'Yeah, I've finished my work'. I would reply 'It's done' if someone asked me 'Is your work done?', and 'It's finished' if someone asked me 'Is your work finished?'. So I guess the response kind of correlates to the way the question was asked?