I'm writing an application where I would like to use a few backgrounds that contain the Android "green robot, and perhaps even one that says Google underneath the robot.
Is this against the terms of service or does it violate any copyright laws?
If it is against any laws, will it matter if the app using the icon is free or charged?
As per the Android Branding Guidelines, you are allowed to use the Android robot icon provided that you give proper attribution (Google's attribution policies).
I'm pretty sure you won't be able to use the Google logo though. Check out Google's Brand Features Terms and Conditions for more info.