4. The round used needs to have minimal wall penetration, because it's an apartment. That's why I've ruled out shotguns.
Shotguns loaded with buckshot are no worse than hand guns or pistol caliber carbines with regard to wall penetration and its an unfortunate fact that ANY worthwhile self defense ammo will penetrate typical interior walls with enough energy left to still be potentially lethal.
I would say there are three choices to consider:
1 - A pump action shot gun, possibly a 20 ga youth model. Load it with #4 buckshot or larger. Avoid 'birdshot' at all costs. It lacks the penetration to be a reliable fight stopper.
2 - A pistol caliber lever action. A 16" Rossi M92 in .357 would be a good choice here. More expensive than the shotgun, perhaps, but a bit lighter and less recoil.
3 - The pistol caliber carbine you mentioned. If its reliable (and I've seen a fair number that weren't) it should make a good choice, too.
Just make sure to take your friend out to practice so she can at least hit near the center of a man size silhouette at 15-20 feet. Even with a shotgun this takes at least some practice.
Just as important, talk to here about her attitude and feelings towards lethal force. A gun is a wonderful equalizer, especially for a woman who may be confronted by a larger, stronger man. It does no good thought (and may do harm) if she is not prepared to USE it. Make sure she thinks about whether she will be able to shoot another human being if she has too. Some people have been so programmed to non-violence that even to save their own lives they can't do it. If so, she might be better off with a big can of pepper spray or a taser.