Does MFRC522 supports native SPI of Arduino Due?
There is no reason why it wouldn't support the Due's SPI. It just uses the default SPI.h library as the interface.

The resetPowerDownPin can be anything you like. It is not part of the SPI protocol but specific to that library. It is just controlled with digitalWrite() internally.

If you don't want to use the functionality you can set it to MFRC522::UNUSED_PIN and it will be disabled.