Translation:Where is the cold medicine?
Hardly is not the adverb form of "hard" - it's a different word that means the opposite. It means "not much", or "just enough" depending on context.
So your sentence as it is: "You are studying Japanese hardly aren't you?" actually means something like "You're not studying Japanese much are you?". (also, some adverbs naturally go in front of the verb, and some after. "hardly" is more natural before - "hardly studying x" is better than "studying x hardly"
The adverb form of "hard" is actually just "hard". To get the meaning you intended, the sentence should be "You are studying Japanese hard aren't you?".
"Where is there cough medicine?" - surely "where is the cough medicine" is "kaze no kusuri ha doko desu ka"? And if you say "kaze no kusuri ha arimasu ka?" you're asking "is there cough medicine" so inserting "doko ni" should make it "where is there cough medicine?"... Even if it is unnatural to say it like that in English, you should not penalise those who make literal breakdowns of the language because it surely indicates a higher level of understanding. Especially when in other circumstances you penalise those who make more general translations that sound more natural in English. Reported.