As a sales person at an FFL, I can answer most of this.
Who exactly is called depends on the state. Ohio and most other states phone directly into the NICS hotline. Some states, Georgia being an example, I think, have a state run line that links into NICS eventually.
The purpose of this is to ID whether you're a person on the FBI's felon/domestic abuse/nut-job list.
From my understanding, all NICS check info are removed from the system every 30 days. This can cause multiple gun purchases in a short time to cause a delayed response (i.e. two handguns in a week, etc) as it flags as suspicious and warrants a supervisor at NICS to make closer look. I've had one guy who had guns stolen from him come up as a delayed while the investigation was being done.
Now, as to the info sent... Everything on the first page of the NICS form is sent, minus the "yes/no" questions. Those are more for the sellers to use to weed out the obvious. Then again, what reasonably intelligent felon is going to answer yes to that?
On the back page, the type of gun (handgun/longgun) is the only part sent.
The gun's make, model, or SN are not sent. Your ID info is also withheld.
Again, from my understanding of the NICS system, how many guns you've purchased is only tracked within the time-frame allowed by the NICS law, which I'm fairly certain is 30 days from a purchase. After that, the NICS law requires that info to be removed from the system. So the actual call into NICS is not registration, but more like asking if there's any reason not to sell person X a gun.
Where you get into a question of registration is the actual NICS form. These cannot be destroyed except after 20 years in the ownership of the FFL. If an FFL shuts down or loses their license, they have to send those forms to the ATF for all eternity, or until the revolution, whichever first.
Suppose a gun is used in a crime. They can get the SN off the gun any number of ways. They then use the Manufacturer's transfer info to track the gun. From manfacture to warehouse to retail, the gun has to be logged in and out of a bound book at every stop. This makes tracking easier to the ATF than computerizing the record, as it removes mistakes at the NICS data entry end. At the point of sale, there's a 4473 or there's hell to pay. The 4473 obviously has your name, address, etc on it.
The only hole in this system is the Face to Face transfers idea. Since no paperwork is filed, they can't track it past the last person to fill out a form. That's why the Antis want to close that. But then again, if you sell a gun to someone who's a felon, there's a good chance you're going to jail also. The last person the ATF comes to in the investigation is going to jail, so make sure you get a receipt and at least a name off a driver's license when you buy or sell FTF.
