He knows that the dwarves there accidentally woke a Balrog, a great demon of shadow and flame. The beast is still there.
When? They needed a lot of saving at various times in the Hobbit. However, the usual answer is Gandalf. He saved them from the Trolls and later the Goblins. The Eagles saved them from the wargs and goblins and you might make a case that Beorn and the eagles saved most of the company at the Battle of Five Armies.
Gandalf was about to jump down into the orcs and make his final stand because he had no options left. If it was not for the eagle rescuing him he would have been dead.
After escaping the Goblins initially during the first attack, he follows the Goblins and their captives to the Goblintown. When the Great Goblin was about to attack Thorin, Gandalf revealed himself, drawing his sword, Glamdring, white emitted burning, white sparks that burned into the Goblins around him. He slew the Great Goblin and led the Dwarves out of the tunnels in the confusion, Bilbo accidentally getting lost along the way out.
Gandalf the Grey is one of 5 Maia Spirit Wizards that came into being somewhere during the Ages of the Stars in Middle earth. Maia's are powerful beings that were created by the Valar (Gods) as helpers of sorts. Maia generally take on characteristics of their masters, which is why other Maia spirits like balrogs, vampires, and watchers; created by the Valar God Morgoth, are evil in nature. Gandalf was ever the traveller of the 5 wizards. He learned from nature and befriended nearly all races of Middle Earth. He was strongly in touch with nature, and often times aided the nature clans of Middle Earth such as the Air spirits; The eagles, and the earth spirits; The ents and huorns. Like all Maia spirits, Gandalf can not die by the passage of time, only by being killed by a force greater than his own. After years of studying the world and travelling afar, Gandalf was approached by Cirdan the shipwright, one of the 3 elves to receive a ring of power., the other 2 being Elrond (Ring of healing) and Galadrial (Ring of Light). Cirdan possessed the ring of fire. Cirdan saw in his wisdom that Gandalf was destined to do great acts of good, and that he was far wiser being that of his wizard order, even moreso than the "book smart" Saruman the white. Upon consulting with Gandalf, Cirdan realized that Gandalf would do greater good with the ring of fire than he would, and gave it to him. This fire ring was legendary I believe either the ring itself, or the fire it produced was known as Arnor, which is why during the battle with the Balrog of Moria, gandalf proclaims himself as a servant of the flame of arnor. This account skips quite a bit of time in which not much of note happens, but nearing the ages of the Sun,great events began to unfold that Gandalf was destined to be a part in. He guided Bilbo Baggins, a hobbit from the shire, through a quest to the far reaches of the eastern mountains of middle earth to combat trolls, goblins, twisted beings of mordor, and even a Dragon. Gandalf then guided Frodo baggins as part of the fellowship of the ring through a quest to mordor to destroy the one ring, and defeat Sauron (Formely a balrog of Morgoth, turned human-like by Morgoth himself as a tool to try and eradicate mankind). During this time, the corruption by the dark lord that Saruman the White experienced is brought forth by the conflict between he and Gandalf. This marked a huge shift of power between evil and good, a balance that nature intends to keep just that; balanced. In the conflict between Gandalf and the Balrog of Moria in the fellowship of the ring, neither gandalf or the balrog was meant to come out alive of this conflict, thus one creature of great good, and one of evil leaving the world, and still maintaining the balance, but due to the shift in power towards evil, Gandalf was brought back to equalize this balance once more. Saruman the white was destined to pick up guiding the fellowship after gandalfs death, but as he was corrupted, gandalf returns to middle earth in "The Two Towers" to Aragorn, Legolas, and Gimli in the forest of the ents as Gandalf the White. He then picks up where Saruman SHOULD have, and sees the quest of the destruction of Sauron through to the end. After the defeat of Sauron, the balance is once again shifted, as nearly all evil from the world has been vanquished, so must a great amount of good pass from the world to maintain the ever fragile balance of life. To make up for the loss of evil, nearly all the elves of middle earth have passed through the great harbour (The grey havens) and taken boats to the Undying lands ("Heaven" more-or-less), where the Valar, maia, and the Omnipotent Illuvatar live. However, even this is not enough, Gandalf himself must board the last of the boats along with Elrond, Galadrial, Bilbo and Frodo, and pass to the undying lands. This ends the life of Gandalf the grey/white.
Gandalf didn't want a burglar, the thirteen dwarves wanted the burglar, to help them get steal back their wealth from Smaug the Great Dragon.
He knows that the dwarves there accidentally woke a Balrog, a great demon of shadow and flame. The beast is still there.
He retains Beorn's interest by introducing a few dwarves at a time, while he is telling his story.
They had escaped the goblin caves and were moving west. They got trapped by the wargs and climbed trees. When the goblins began to set the trees on fire, the great eagles rescued them and carried them off.
Bolg was killed by Beorn who was in his form as a great bear. Beorn scattered the bodyguard and pulled Bolg down and crushed him!
The dwarves are happy because they are treated well with great houses.
When? They needed a lot of saving at various times in the Hobbit. However, the usual answer is Gandalf. He saved them from the Trolls and later the Goblins. The Eagles saved them from the wargs and goblins and you might make a case that Beorn and the eagles saved most of the company at the Battle of Five Armies.
Uh.. Bilbo Baggins, to state the obvious. The thirteen dwarves' names are as follows: Fili, Kili, Bifer, Bofer, Bombur, Gloin, Oin, Dori, Nori, Ori, Dwalin, Balin and Thorin. And then there's Gandalf the Gray Wizard, and Smaug the Great Dragon.
Dunno. I can think of a Latin one: Deus Ex Machina. God from the Machine in Latin, which refers to a Greek and Roman dramatic practice of having gods descend on pulleys and winches so as to suddenly appear and resolve matters on stage. It now is used to describe a person or thing that suddenly and unexpectedly sends the plot in an entirely new direction. I'm not sure if you're referring to Gandalf's rescue of the dwarves (in which case, Gandalf suddenly appearing in the throne room of the Great Goblin makes him the Deus Ex Machina) or Gandalf and the dwarve's rescue by eagles (in which case, the eagles are the Deux Ex machina).
That restaurant had a reputation for great seafood.
because the trolls were about to cook then eat them
Giant spiders, reportedly descended from Ungoliant, and relations of Shelob, the great spider in The Lord of the Rings. The Dwarves and Bilbo ran into them when they strayed off the forest road against the advice of Gandalf. The original account can be read in Chapter 8 of The Hobbit "Flies and Spiders." Or you can read a summary of the chapter at the related link.