Processing should handle most of that stuff. Everything you create with Android Processing is geared for Android 2.1 or higher- you can change that but it isn't necessary in most cases. As far as I can tell, the debugging parameter causes the app to quit on backbutton press and adds other features for getting out of the app in case of a serious crash. So you betatest it with the debugging parameter and only remove it when you want to package up the program to ship it to the android market or somewhere else.

NOTE: if you have the latest Processing, you can just Export it (under file) and skip most of the steps that used to be necessary.

ANOTHER NOTE: If you just want to get your app running on your phone, you can go to Present Mode, or Run on Device as it is changed to in a later version. After running it once, you can access it again by viewing all of your apps.

Thanks for the answer! My original idea was to create the apk and test that by directly installing it on a phone, I assume that is too dangerous as the debugging parameter will be turned off and the application could fatally crash? 

If the app fatally crashes, the window will close and an error message will pop up saying what has happened.
The only way the phone could get wrecked is if the app messes with vital information or gets stuck in a loop that cannot be escaped from. Then the worst that can happen is that you have to reload an image of the OS onto the phone which would be fine unless you have important data stored there... But that is only possible if you mess with File IO and you need to enable the sketch permission WRITE_EXTERNAL_STORAGE in order to do that and if the app is not in debug mode and that permission is enabled, the user will have to chose to allow the app to run.
Again, if you just want to test your app, keep it in debug mode and you can even still show it to other people without it being anywhere near your computer and the only way it will make a difference is if you make heavy use of the backbutton.