Help setting up RFID reader with hard to understand schematic with arduino UNO

Have you tried other baud rates, as I told you to in Reply 5?

You are clearly not using SoftwareSerial as I told you to do in Reply 5.

Jumper wires don't generally make good connections in pain circuit-board holes. If you want to use jumper wires for everything you should solder female header pins (like on the Arduino) into your RFID card.