You all seem to forget the most important thing; it's a video game. While they do try to keep it realistic, most of the time you have to go to hell with realism and use a bit of fantasy/science fiction to let the story progress.
Some enemies can shoot a lot of bullets at the main characters, and yet none of them get killed by it, whereas in the real world, one can be sufficent to kill a person. If getting shot by multiple bullets won't kill you, getting impaled in the shoulder by a magical ice shard probably won't kill you immediately either.
As for how Squall got healed, as it was already mentionned, Edea wanted to know the real meaning of SeeD. Letting the guy who may detain the information you want die isn't really a smart move. It's plausible that Edea, through Seifer, asked that Squall and co. be healed, questioned, and if necessary tortured in other to get the information she wanted.
