The world of J.R.R. Tolkien in which his books The Hobbitand The Lord of the Rings are set is called Arda. Middle-earth is actually a continent in Arda, but the name has been used to refer to the whole fictional world. (IIRC, the world is not given a name in the actual Hobbit book itself, since Tolkien only integrated the Hobbit into his older Middle-earth world after he has already written it.)
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The events of The Hobbit takes place in Middle Earth. It starts of in The Shire, the land of the hobbits.
Beorn
I believe that the goblin king is named Bolg, son of Azog
Bilbo's ponies name was Myrtle
THE GREAT holy hole
A hobbit barrow is referred to as a 'smail.'