You pulled off a great Jeopardy! challenge here. Nicely done.
I think there's some playability issues with the other encounters, though.
I found the grid-iron encounter a little unclear. It would have helped to have more detail on the diagram: where are the red and yellow flags? Where are the opponents and player positions?
I think the 1 hour timer is not enough time - I can see a good chunk of that being burned up just explaining and clarifying the first encounter alone, since it is a fairly novel challenge. Would definitely want to play test and up the time limit if needed.
The biggest area of improvement I can see though is the premise. There's a lot of unanswered questions and it feels non-sensical. What is the purpose of the flying city? Why does it have these game masters and challenges in it? What is the final boss hoping to achieve? What became of the previous people sent to solve the problem? What happens if the PCs succeed? I think if you put in a background section and explained the events/causes leading up to the current predicament it would help a lot.
I also think it would be cool if the players had some more options to play around the challenges, rather than be railroaded into completing them. The social manipulation for Lady Query was a great start, would love to see more of that kind of stuff. Mess with the flying dude's flying apparatus, allow a people to break through the doors to the next area if they use smart team work, etc.