It could go either way: Claire could die, and Kate adopt Aaron, or Claire stays, but lets Aaron go (though I opt more for first situation, as I don't see her wanting to be separate from Aaron).
As for why Jack is upset : no idea, except that the writers wanted us to think that he's upset because it was the other guy's baby (or even his own).
Things keep getting even more mysterious, don't they? Like why are the survivors saying that only 8 people survived the crash? To keep those who decided to stay safe? (as the previous episode might suggest).