Can android.util.log do a rolling log like I'm requesting?
1) Not like you requested. The logs will be rolling but for all applications on the device, not just your app.
Where does android.util.Log write to by default?
2) The Android logging system, which can be viewed through logcat. Think of it like the Windows Event logs if you are familiar with that. I would download a logcat program and scroll through your system logs to familiarize yourself with them.
If just to console, is there a way to write this to a rolling log file on the android device, which can then be emailed if there is a problem with the program?
3) You could write your own rolling log to the filesystem and then email it. However, you would have to implement this functionality. You could also try seeing if there are any 3rd party logging tools/libraries that may satisfy your needs.