1. The 4473 paperwork is the domain of the BATF. The document is retained by the FFL. The only time it may be viewed by an ATF IOI (industry operations investigator) is during an inspection of the FFL, as the result of a trace request/criminal inquiry, when the FFL has ceased operations and all the 4473s are boxed up and shipped to West Virginia, or, if the FFL has majorly fouled up and their life & records are being torn apart in the course of a criminal investigation.
2. NICS checks are the domain of the FBI. Data is not shared between them, by law, during the firearm sale/transfer. The check can be done by phone or via computer. ATF is encouraging FFLs to use the computer system, but it is not required.
All the FBI NICS system knows about your firearm purchase if it's one of the following:
Sale of Handgun
Sale of Long Gun
Sale of Other
Pre-Pawn of Handgun
Pre-Pawn of Long Gun
Pre-Pawn of Other
Redemption of Handgun
Redemption of Long Gun
Redemption of Other
Private Sale of Handgun
Private Sale of Long Gun
Private Sale of Other
Private Sale Return to Seller Handgun
Private Sale Return to Seller Long Gun
Private Sale Return to Seller Other
3. If you transfer/purchase more than 1 handgun within 5 consecutive business days, a 'Report of Multiple Sale or Other Disposition of Pistols and Revolvers' ATF Form 3310.4 is generated. One copy goes to the ATF. One copy goes to the Chief Law Enforcement Officer for your area. And, the third goes into the FFL's files just like the 4473 does.
As a border state, Type 1 FFLs have to generate this same form for the sale of one or more RIFLES in caliber greater than 22. However, in a weird quirk, Type 7 (manufacturers) are exempt--according to the IOIs--from this reporting requirement...although your friends at the ATF would really like you to
Are there any more points of confusion that I can clarify on the sale/transfer end of things?