The fob is the remote lock+arm / unlock dongle that is round and normally is on the keyring with the gtr key.
You can reprogram a new fob with a complex procedure involving sitting in the car and doing various things with it, and the ignition and the doors. But you can do it yourself. The function of the fob is mainly to operate central locking. I don't think that by itself it can do much to the factory immobilizer. It can arm it, but not disarm it. Not sure.
The ignition key itself has a chip in it, and there is a receiver for the chip ("amplifier") in the steering column. It communicates with the NATS (nissan anti theft module) which is located down further in the dash, and is connected to the red LED, the ECU and the ignition, etc.
If the key is broken (does it have a battery? unclear) or a new key is used, or for some other reason the key cannot by queried by NATS when it is inserted into the steering column, the factory immobilizer light will go solid red and "the car will be difficult to start" (unclear what this means). The NATS also has a line to the ECU, so it compares notes with the ECU somehow. If the ECU has been swapped this will also make NATS go red.
To reprogram the chip in the key or to activate new keys you need the nissan consult II unit. It involves reading a pin number off the car, entering it, getting back some other code, etc. I believe that the nissan consult II needs a memory card specifically for NATs to do this. I'm not sure if a regular nissan dealer has the correct card or not.
Things I don't know yet are what exactly NATS does if it is activated: does it pull power from the coil packs? (crank but no spark) or does it tell the ECU not to start (so a third party ECU can ignore this) or does it do something else?
Consult II has a bunch of diagnostics for NATS that can trace various problems such as the steering column amplifier not working, the communication with the ecu not working, etc etc.