From what I remember, Robert simply got too drunk to hunt. His Lannister squire made sure he kept drinking. No poison was implied.
As for the Arya story arc, they're growing her influence and experience. If she just ran home to the family as an 8-year old (or whatever she is now), she'd just be a frightened child. No, they're making sure that she's meeting people, having experiences, etc., so that by the time she's older, she's a mad bad ass-kicker with a lot of friends.
What I'm a little unclear on, is who's going to win when it's Arya vs Daenarys? That's my guess for the final confrontation for dominion of Westeros.