I've read that the official Android Market in-app billing mechanism can only be applied to applications published through Android Market. If I release my APK (the same copy) on Android Market and also via other distributors, would the billing mechanism still work for my APK which is distributed outside of Android Market? If so, is there any reason why this strategy might be ill-advised? If this strategy is ill-advised, can anyone suggest an Android in-app billing mechanism which has good international coverage and which can work across the different market places?
No, it won't. The in-app billing code depends on a remote method, exposed by the Android Market application. If it is not available on the device, or the app has been installed through another channel, you can't use in-app billing. Plus such usage is probably in violation of the Market's terms of service.
You might want to try PayPal, they have an Android API for micro-payments.