"Why did you sit here?"
Translation:Neden buraya oturdunuz?
you can use it but there is actually a nuance. the verb of sitting implies a state, while the verb of sitting down involves a movement into the position of sitting. therefore in my opinion you should use dative case for sitting down and locative case for sitting.
so, in my opinion the translation should be reverse as you mentioned. but still i'm not native speaker of english so i don't really know, maybe they are interchangeable.
I agree about the existence of a nuance (buraya vs. burada), but it seems to me that either would work here, because English doesn't really distinguish between sitting, the state, and sitting, the action. That is, if I say, "I am sitting," I could mean either that I'm already seated (the state), or that I'm in the process of seating myself (the action), and the same is true if I say, "I am sitting down." (Using "sitting" or "sitting down" can create a difference in the tone of the sentence, but it doesn't really change the meaning.)