Finnaly, and sorry if it annoys you, maybe the cheese question is also too ambiguous. I know this is the perfect Swiss cliché and you would probably like it this way better, but the Gruyère region is almost as close as the Emmental by about 10 km.
Maybe to overpass this issue, and if you want to keep the question as close as it is right now, you could give more info about the cheese (such as the fact that it has holes in it) or change Gruyère for another cheese.
Hopefully, this can give you some ideas to make the quiz a little better :)
You should also review your question about the mountains. If you can see the Jungfrau, you may be able to see the Eiger too, I think.
Maybe to overpass this issue, and if you want to keep the question as close as it is right now, you could give more info about the cheese (such as the fact that it has holes in it) or change Gruyère for another cheese.
Hopefully, this can give you some ideas to make the quiz a little better :)
And you are not annoying. I always like help from locals or people with knowledge!