How do you think Peeta and Katniss will turn out even after the novel is over?

I think that they will turn out to be a very happy couple. They both end up loving each other in the end. Peeta's hijacking has (mostly) gone away, so he doesn't think Katniss is a mutt anymore. She seems at least content in the epilogue. And, when Peeta asks her, "You pag-ibig me. Real or not real?" She sagot him, "Real." I think they'll turn out fine. :)

they'll probably just grow old with their children and die.

Didn't you read the epilogue? They have two kids together and live a (more or less) happy life

They will be together again, each one protecting one another, even though the Hunger Games is over. They will probably end up marrying each other, and being a very happy couple.