Cool, that's a nice build.
Basicaly the parts are all the same. However, when ordering parts, pay attention to weither they are "Mil Spec" or "Commercial Size" parts (different size parts). The best reasson to use a Carbon-15 upper and lower is weight. The Car-15 is substantually lighter and easyier to use as a pistol.
Car-15's use to have very bad reps, because of the mfg that went out of bussines that made them. The product line was bought up by Bushmaster and they have substantually improved the product. In fact the only Carbon parts on the new guns are the casing for the upper and lower, the stock and the hand guard. All the other parts are metal. People use to complain about there not having a foward assist and dust cover, the new ones have both.
I am unsure on the barrel length restriction for a pistol, but I believe it can not be longer than 11 inches for a pistol or shorter than 16 inches for a rifle. And a pistol can not have a stock or a vertical grip on the front of the pistol.
Lowers can be made into pistols or rifles, but can not be changed once it is registered, and yes it will be stated on the form you fill out for purchase of any weapon and kept by the retailer of the lower.
To eleminate the need for the takeup (recoil tube and spring) you could go with a piston system instead of the normal gas system. This will make your pistol shorter yet, lighter and eleminate the tube from the back of the weapon.
The new Carbon-15's I personally think are great buys, fun to shoot and very accurate. My christmas present this year was a Bushmaster SuperLight Car-15 carbine (16 inch) in 5.56 Nato. It was on sale for $599.00 and I spent another $135.00 on add-on parts (Butt Pad, Houge pistol grip, bipod, vertical pistol grip and quad rail)
They are easy to build and fun to use. This is what mine looks like.
Good luck and have fun.