All private dealers conduct background checks. FFL's have NICS checks in gun shows.
1. Automatic pistols aren't automatic.
2. Your proof?
3. $600? I paid a lot less for mine and it wasn't junk.
4. Then why did they call the FBI when I bought my rifle?
5. WTF do you consider a cop-killer bullet.
6. One person...
7. "Unlicense dealer?" That's a felony.
8. Pure Puffery
9. Unlicense dealer is a felony.
10. Don't you need a Class III for conversion parts?
11. Bullshit.
There is no such thing as a private dealer. If you are a dealer, you must have a FFL, and conduct the NICS check, at your place of business, or at a gun show. (With some exceptions, such as purchases by those with CHL/CCW from certain states, like Texas for example).
That said, collectors and/or hobbyists can sell guns, at a gun show, or elsewhere without conducting any check at all, at least in the Free States. YMMV. (It would be good to check a driver's license, since even for individuals, sales to out of state residents may be illegal.)