"Where is a big department store?"
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!
That is a nice explanation in general, but i still don't get why we used おきな 病院 in all the examples of the use of ooki/-na before, but now it's おきいアパート. So, dince they both are buildings, there really is no rule to the usage before the noun, it's just my choice of style? Or just another inconsistency of the owl?