Native English speakers tend to avoid answers like (C), especially if -- as usual -- the explanation clause is left off and the answer is reduced to only Yes.
The rule is that, for the most part (i.e, I can't think of an exception, so I'm hedging), Negative Yes/No questions (not, btw, "negative-polarity") get answered Yes or No just as if they were affirmative questions. Since logic doesn't deal with questions, the negation has no logical force.
It's just there as a conventional marker to express the speaker's belief that the answer should be Yes. Negative questions are often used in rhetorical questions not meant to be answered by anyone but the speaker -- "Now, wouldn't this look better over there? ... Yes, it definitely does." Language never lets a useless convention go to waste.
So, (C) is not right, (A) is fine, and (B) doesn't make any sense, since it says we'll park instead of we parked; with that correction, though, it's fine too. And just Yes for (A) and No for (B) are fine and normal, too -- though it's always safer to clarify an answer if there's any possibility of doubt.