Not so much, apparently the WS2812b lights up white when it has no Input signal.
As stated before, if you have it the way you've drawn it should work. Have you tried powering the Nano with the external powersupply ? (rather than USB) The most suspect to me is the common GND between the nano and the rest. Can you verify with a multimeter that it is actually connected properly ?
Just to check i looked at your code, and saw
void setup() {
pinMode(led, OUTPUT);
pinMode(LED_PIN, OUTPUT); // this is obsolete
// doesn't change anything of course, but FastLED sets the pin to output already
FastLED.addLeds<WS2812B, LED_PIN, GRB>(leds, NUM_LEDS);
FastLED.setBrightness(10);
}