Hello Tado,
You can power the arduino using battery or 9v power supply from wall socket.
"Can you download the sounds and then unplug the USB cable?"
I don't think the arduino has enough memory hold mp3's even if they are short drum sounds, you might either need to extend the memory on the board or get a shield that does the job for you, I suggest looking at adafruit or clicking this link it was suggested in an earlier post and might be what you need: