Thank you very much for your fast reply PaulS! 
I think I understod your advice regarding the begin() and init of hardware in a library.
I fill only the variables inside the constructor and afterwards I call the begin() function in the
setup-function to init the hardware:
CPP:
FadeLED::begin()
{
  pinMode(_pin, OUTPUT);
}
Sketch:
#include <FadeLED.h>
FadeLED myLed(10,50);
void setup()
{
  myLed.begin();
}
void loop()
{
  myLed.fade();
}
Is this correct?
Unfortunately I dont really understand what you mean reagrding the array declaration especially
your statement:
You need to have 64 lines to initialize each element.
Could you post an example how to declare an array inside a library?
Is the array declaration the main problem of my compiler error?
Thank you!