what plan does Bilbo carry-out? whay does he do this? What does this reveal about his character?

Bilbo steals Smaug's cup. This distracts Smaug so the others can eventually get to the treasure. This reveals that the little thief Bilbo has more courage than most of the others.

Bilbo gave Thorin's Arkenstone to Bard. He gave it to them so that Thorin would give them the part of the treasure they deserved.