Ok, got that 
I need to use the computer's USB to uplaod the sketch to the board, although only once, as I swith to the powerbank after that, but I can't passby that step.
With this latest testing, only the mp3 player and the 3W speaker are conected to the Arduino Uno.
On previous testing, also 42 leds (3812's) were connected, that flash on and off on a 60% brightness, although not all at once.
Ok, seems a good idea. The quest for a 2A phonecharger has begun.
It is probably also best to have separate powersupplies, when I hook up the leds as well. They work great with my current powerbank of 1A.
Maybe I can try to install a step-up booster that delivers 2A und still use my actual powerbanks?