The background check is the best tool available, but not perfect. What other indications are you concerned about? I've seen people get turned away when it was obvious that the person buying the gun wasn't the person picking it out. Reputable dealers don't want to lose their livelihood or go to jail.
That idea doesn't work at all. I just grabbed some ammo our of my stash. Tell me which ones are for a pistol, an AR, a bolt action or lever action?
L to R and what I shoot them from
30-06 - Bolt gun, Semi Auto rifle
.35 Rem - Lever action, pistol
.300 Blackout - Semi Auto/AR, bolt gun, pistol
.223 Remington - Semi Auto/AR, bolt gun, Pistol
All have similar velocities depending on the load
30-06 2700 fps
.35 Rem 2250 fps
.300 Blackout 2375 fps
.223 2775 fps
I should have thrown in a 12 gauge slug that can be shot out of a bolt gun or semi auto at over 2000 fps and more destructive than anything in that picture.