If a hero opens a chest, and as OL i play a trap card that kills the hero on that turn, does that hero get to distribute contents? if not, what happens?

The chest is still technically opened, as it's the trigger for your trap. So yes, the heroes still get to distribute the contents and the dead hero goes to town.

Aye. It states in the Rule Book that even if the Hero is back in town, they still recieve a share of coins and/or treasures. Being killed doesn't prevent that.