I pulled out my Genki I to see if it would help clarify the issue here. :D I don't think the grammar section is laid out as well as some of the later grammar points are.
All of these questions have the same basic format: (place) に (thing) が います/あります か。
This is a basic format that will be very important for you to learn. Even my mom (who doesn't speak a word of Japanese) has learned to recognize "Toothbrush がどこにありますか~!!!" ;D [size=5pt]I take that back. She knows how to say わかりました from too much Shogun. -.-;;[/size]
The nature of your questions shows that there is a small gap in your understanding of the questions. To check your general understanding, as opposed to maybe just having a problem with this particular kind of sentence, did you interpret the first few questions along these lines?
1. あなたの町に日本のレストランがありますか。
Is there a Japanese restaurant in your town?
2. あなたのいに猫がいますか。
Does your household have a cat?
3. あなたの学校に何がありますか。
What is there at your school?
4. あなたの学校に日本人の学生がいますか。
Are there Japanese students at your school?
If not, a quick review would be in order. Even if not, a quick review never hurts.
With both います and あります, the thing or person that the verb acts on is marked with が. So います is used when (thing) が is a person, and あります when (thing) が is an object. This is in no way influenced by the place marked with に - as Daniel pointed out, the word marked with に indicates the place in which the person or thing exists.
When you're trying to figure out a sentence, break it up into parts by particle - in this case, デパートに, 何が, and ありますか. Look at the verb first to figure out how the particles interact (あります, so が marks what is arimasu-ing, and に marks where it happens), match that up with the pieces (何が, so they want to know what is arimasu-ing, and デパートに, so it's happening at the department store), and put it back together. That's how I remember getting through several chapters of Genki I.
So a breakdown of the specific questions:
5. デパートに何がありますか。
What is there at a department store?
7. 動物園に何がいますか。
What is there at a zoo? (This should clue you into the answer, just as it clued you into the fact that you were missing something - just remember, animals are living too, so they can fall under います.)
9. あなたの家に何がありますか。
What is there at your house? (Like above, but backwards - make sure you don't say you have a brother at home, unless you're being really snide about him being an "it". ;D)
Really long response, but I hope somewhere in there it helped something click for you.