I'm currently developing an AIR application (FlashDevelop & Flex using Flash/AS3.0), which is in this case a game. But it seems that I can't get hardware acceleration in full screen mode? Does this mean that setting displayState to full screen is not enough in AIR application or AIR application does not support hardware acceleration? When I launch the same game with the standalone Flash Player then hardware acceleration is on.
If you set the fullscreenSourceRect, you will get hardware accelerated scaling, but that's the only form of hardware graphics acceleration currently supported by AIR.
To save data locally with Flash, you can use FileReference save() and load() -- the user has to initiate the operations directly, though, so you couldn't auto-save. If the data isn't very large, you can use shared objects.