Is it true that I do not need additional pull up resistors if I connect an I2C slave to pins 20 (SDA0-3), 21 (SCL0-3) of the Arduino Due? (On the Arduino Due schematics it is noted as "I2C Voltage Translator".)
Yes. You do not
need to add (nor should you) any additional pull-ups anywhere in this I2C bus. The resistors on the DUE are very aggressively sized (small). Adding any additional pull-ups on the I2C bus could destroy these IO pins. Also, the last time I checked, the print says that they are 1.5k pull-ups. However, in reality, 1k pullups are installed on the PCB (double check to be sure).
If I use the Wire-Library the I2C communication is via pins 20 and 21 ?
How do I do (which library) I2C communication via pins 9 (SDA1 = TWD0) and 10 (SCL1 = TWCK0) ? There are no pull up resistors for pin 9 and 10?
It's the same wire library. Do a quick search for "wire1" for solutions. Also, become familiar with the limitations of the current wire library, as many of the lower-level (more advanced) routines still do not work.
In addition, yes, you will
need to add external pull-ups for SDA1/SCL1.