Hi,
1. To build for mobile devices you need to use AIR, which is essentially Flash with some extra configuration and if you want to, some extra API capabilities. You do not need to make any platform-specific modifications to your code, so the exact same code base can be published to both iOS and Android.
2. If you use AIR it will run as an application on all platforms that AIR supports, which is mostly everything. If you use Flash it will run on all platforms that have a recent enough Flash Player installed (11.0 to be specific), and that does of course not include iOS which doesn’t support in-browser Flash, and also not Android which does not support the 3D APIs that Away3D use.
Bottom line, if you use Flash (for browser) you can target both Windows and OS X. If you use AIR (to create applications) you can target Windows, OS X, iOS and Android.
I’m not sure about Linux support these days, but I don’t think that the 3D APIs are supported on Linux.