What does Thorin vow to do to anyone who withholds the Arkenstone?
Thorin vows to avenge anyone who withholds the stone thus frightening poor Bilbo who is now in possession of the priceless gem.
Who was the "thief in the night"?
Bilbo Baggins was the thief in the night.
How was Bilbo able to escape?
The hobbit persuaded Bombar who was acting as night watchman to abandon his post temporarily. Bilbo accomplished this by telling the dwarf he would be happy to fill in for him until midnight as he wasn't feeling sleepy himself.

Once the dwarf left, Bilbo put on his ring and slipped down the walls using a rope.

Why did Bilbo give the Arkenstone to the Bard?
Bilbo knew how much Thorin valued the gem and he realized the Bard could use it as a bargaining tool to speed up the negotiations. This would allow Bilbo to collect his share of the reward and return to his home as soon as possible.
Who delights Bilbo with his presence just as the hobbit is preparing to depart the camp for his return to the Mountain?
Bilbo receives a clap on the back from Gandalf