Many states allow person-to-person gun sales for state residents without going through an FFL. The first time a gun is sold that way and the serial number is useless for tracking purposes.
Depends. When I do a person to person sale I generally require a receipt that contains the names of the parties, serial #, and date of sale. If I buy a gun and find out it was previously used in a crime I want to be able to document when I got it. Same thing if I sell a gun and it is subsequently used in a crime. But the government doesn’t know about the receipt unless for some reason things come back to me somehow.