Hi! I have problems with reading RFID tags.
You have more than that. You have not explained what Serial and Serial1 are connected to.
If Serial is connected to the PC, and you are sending data to the Arduino from the Serial Monitor, to tell the Arduino to deal with Serial1, you then WRITE to the Serial1 instance, where, presumably, the RFID reader is. What does that have to do with reading RFID tags?
So, you need to clarify what is connected to what.