I have only heard the one defintion for assault rifle, and I'm sticking to it. (BTW, the .223 is just small, not abbreviated, so maybe doesn't strictly fit either).
Anyway, by this mesure, the M1/2 Carbine sounds like one to me. A .30 cartridge was requested, but attenuated so that the gun is lighter and recoil less. In fact, the only reason it might not be is the intent. We wanted the gun as a PDW -- an upgrade to the pistol -- instead of a firepower shift (increase?) for the infantryman.
The first, hard to nail down without research. There was lots of work in this regard in WW1 and even a tad before. Experiments like lightened Lewis guns and Maxims (!) for trench warfare raiding parties, for example. Even by then the Germans had discovered the SMGized pistols didn't have the stopping power required for a battlefield, so wanted something like a rifle cartridge. They never quite got there till the StGws appeared, but there you go.
If you disregard the cartridge thing, how about the FG-42? Do design principles have anything to do with it? Straight-line stock, detachable mag, etc.? Cause I hardly think the Mini (ok: AC-556) fits assault rifle; just being smaller than a battle rifle doesn't exactly make it an assault rifle to me....