Also, I can install my app on the "iPad Air" simulator but the app quits once the default screen shows up. My app runs fine on an actual device btw.
One thing that might not be clear is that you need to package your app differently for the iOS Simulator. The same IPA file can't be installed both on a device and also in the simulator because different CPU architectures are involved.
Normally, you might set the -target option for ADT to something like ipa-app-store or ipa-debug to deploy to a device, but you need to set the -target option to ipa-test-interpreter-simulator or ipa-debug-interpreter-simulator for the iOS simulator. You also need to specify the -platformsdk option. If you're building from an IDE, it should expose these options somewhere.
See Adobe AIR: ADT package command for details.