Two more things: (1) If you are weak in Rpi and python, AND your schedule is tight, you might like to consider (a) libnfc-1.71. I2C mode, which I found OK, (b) Arduino library, which is very mature and easy to find support, (c) Buy more boards to stand by and/or cross check.  Reference: Arduino library for MFRC522 
https://github.com/miguelbalboa/rfid

Before buy:

Please notice that there are many sellers (ebay, aliexpress, ..) who sell mfrc522 boards. The quality of these boards are extremely different. Some are soldered with wrong/low quality capacitors or fake/defect mfrc522.

Please consider buying several devices from different suppliers. So the chance of getting a working device is higher.

If you got a bad board and you can tell us how to detect those boards (silk, chip description, ..), please share your knowledge.