What am I doing wrong???
You wrote WAY too much code, and have way too much hardware, for a system that doesn't work.
You did NOT tell us how you actually connected the RFID reader to the MEGA. You tell us that by posting a schematic and by posting a picture that proves you followed the schematic.
The picture should NOT show 4 foot long wires all bunched up, all the same color, running out of and back into the picture, which is poorly lit and out of focus.
The code should do NOTHING more than prove that you can read a tag. No relays. No LEDs. No alarms. And ABSOLUTELY NO LCD. NOTHING but the RFID reader should be attached to the Arduino.