Okay, thank you for the quick answer. I use IDE 1.6.8 with AVR Boards Version 1.6.14 and 1.6.7 for MKR. The LED and the MKR are supplied by an extra regulated power supply at 5V.
The Datasheet to the MAX7221 can be found at e.g.
The second code example only uses build in libraries and should switch all the led's on ... in the test mode. So we can focus on this for debugging.
Currently, I don't have a detailed schematics, but I'll create one, if necessary. As already mentioned, it's working with a ArduinoNano, so maybe it's sufficient to create the schematics only of the MKR1000 part and the SPI connection?