http://www.nicoclub.com/FSM/G35/Sedan/2003/ec.pdf
P1212: (page 508) TCS COMMUNICATION LINE
U1000, U1001: (PAGE 142) CAN COMMUNICATION LINE
P1612: Nissan Anti Theft System (NATS) ; This code means you have a chip issue with your key. In effect the anti-theft immobilizer system is not reading your car keys. This must be repaired at the dealer as they will have to reprogram the immobilizer to your keys.
The top two indicate a open connector or break/short in the communication system. This could also be due to a bad battery, poor grounds, etc. The NATS issue could also be caused by the communication issue within the car and not a problem with the keys.
P1212 says to run the tests via the U-codes on page 142 of the linked pdf. Start there and see if that gets you in a proper direction.