Ar15 pistol
OK, IT DEPENDS ON YOUR STATE.
For free states, if you fill out the 4473 and just purchased a receiver, bare, stripped, Etc. it should just be marked 'receiver/other' on the 4473. Then it can be built as either, as long as you don't build it into a rifle and then convert to a pistol, you've done no wrong.
And you can possess pistol barrels, I just would not store them with my other AR's and I damn sure wouldn't build a pistol upper and toss it in the safe with all my rifles, no way.
Jeez, what a clusterfunk.