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You need to remember, that for your Android device, Flirc is not an IR receiver, but a keyboard. You can only do what's available from a normal keyboard. The original remote on the other hand uses a different input channel - probably there's some kind of system app which interprets IR commands from the original remote and has deeper access to the system itself. The mouse feature is probably some kind of mouse emulation, where you switch the mode and then control the mouse pointer using direction keys. I think this is not possible in Android by using only a keyboard.

Hi, Flirc doesn't support mouse events so point 3 is not possible. As for the Home button, you can use FireTV controller in the Flirc GUI. It has an Android compatible Home button. Not sure about the power button though. You can try using wake/suspend button on the Media Keys controller.