StandardFirmata on Due

Valdas:
But I can't test using http://www.pjrc.com/teensy/firmata_test/firmata_test.64bit program, becouse window is empty.

In the screenshot you posted, notice there are 2 menus at the top, "File" and "Port". Try using "Port" to select the serial port. Of course, close the Arduino Serial Monitor before you open the port with firmata_test.