All three of your sentences are fine but they have different meanings.

Short answer: I still haven't finished yet. I don't see why you can't use it.

It's a bit strange to use both of them together, as they mean the same thing.. that's all. :)

Yet is time. Not yet, maybe later. Still is often about repetition. Asked before. Still not done. Ask again later. . In normal conversation, one is usually enough. For special emphasuis of both meanings, sure, emphasise away. Good answers below. Got the idea yet? Still not? :)

If you use them both in one sentence, it would imply that you already had one conversation about not being finished. Now you're saying that you STILL haven't finished yet. Otherwise it would be a bit redundant.