"Where is a big department store?"
Because desu is not a straight translation of "is". It's more a polite ending a lot of the time. Doko desu ka or doko ni arimasu ka, but not doko ni desu ka.
Please don't rely solely on duo for learning any language. It's a good start and supplement, but if you really want to learn, you would be better off investing in a good course. Tae kim has a great guide you can buy, or download from his site for free. There's way too much duo misses out on (like how to use desu and da for example!) especially if you use the app (still can't believe no tips and notes yet!)
I could be completely wrong here, so someone can comment on if this is right, but the use of ___はどこですか sounds more like you know the object in question already exists in area and are asking where it is. Meanwhile, this question is asking if there is one, and asking where it is at the same time. I'm inferring this based on the fact that ありますか is like asking "Is there?"
This English question doesn't sound very natural either. I personally would have split it into two phrases "Is there a big department store here?" "Where is it?"
大きい and 小さい, being antonyms too, act like both i-adjectives and na-adjectives. That being said, careful not to mix up their usage! 大きい can be used both as an attribute and as a predicate, but 大きな only as a predicate! Take a look at this:
A: あの大きい雲は見えるの？(Can you see that big cloud?)
A: あの大きな雲は見えるの？ (Can you see that big cloud?)
These sentences are the same. The adjective is used as an attribute. However, if speaker B was to reply with “Yeah, that cloud is very big!”, 大きい would be the only correct choice!
TL;DR 大きい can be used both as attribute (in front of the word) and predicate (at the end of the sentence). 大きな only as attribute!