I moved your post over to the AR section- you had posted in the area that deals with software for the website.
With ANY rifle caliber handgun- the shorter the barrel, the less the velocity, the more impressive the noise and muzzle flash. Eventually you could get to the point that a jagged rock would be more effective.
As far as the pistol-rifle-pistol thing- You will need to start with a virgin AR-10 frame, or one marked pistol. An AR-15 frame is not going to work, of course. If you start with an AR-10 RIFLE, remove stock, shorten barrel below 16 inches, etc- then you have manufactured a short barreled rifle. which needs approval from the ATF and payment of a tax BEFORE you build it.
If you start with a pistol, you CAN install a longer barrel, and stock, etc, Building a rifle from a pistol is not illegal. Can you change it back to a pistol again? The legality of THAT has been argued both ways. I would urge you to get a written reply from the ATF Firearms Technical Branch in West Virginia. NEVER have a firearm with a buttstock and a barrel under 16" unless you have your papers in hand from the BATFE.
Last- the AR-10 is not as standardized as the AR-15, You will encounter parts from different makers that will not marry up.
Oh- one more thing- I do not know you, so I mention this- you must be 21 to purchase any firearm other than a rifle or shotgun from any dealer. That includes a bare virgin receiver.
What we have here is... failure- to communicate.