Why did no one save Thorin when he was wounded, instead of talking? Bilbo never called Gandalf or anyone to help him recover. Gandalf, Elrond, Galadriel and Saruman would have killed all the orcs and helped Thorin, but no one came.
In The Hobbit, there is a very particular reason why Thorin is difficult to rescue. Tolkien does not emphasize this point, but it is clear if one looks at the geography of the battle. The Battle of Five Armies sees the goblins and wargs coming from the north, around the Lonely Mountain. The men of Esgaroth, the elves of Mirkwood, and the dwarves of the Iron Hills wait to fall upon them when the wargs and goblins come down between the ridges on the south side of the mountain. However, the thirteen dwarves coming from inside Erebor enter the fight from a different direction. Part of what makes Thorin's unexpected charge effective is that he and the others fall upon the goblins from above and, more importantly, from the rear. This allows the dwarves to cut through rank after rank of enemies, until they reach the strongest goblins, surrounding Bolg of the North, where their advance is balked.
Other goblins and wargs close in behind them, leaving the King Under the Mountain and his compatriots pinned against the bodyguard of Bolg, son of Azog. Fili and Kili give their lives to protect Thorin personally, as he is not only their lord but also their uncle. This buys the king some time, but rescue is still slow to arrive. His group is completely cut off from the other dwarves, elves, and men. What made their attack effective was it coming from the enemy's rear, but when Thorin's advance is stemmed, this geographic fact changes from an advantage to a liability, since Thorin is separated from succor by a large bulk of hostile troops.
It takes an ally of tremendous power, Beorn in bear form, seemingly grown to superursine size, strength, and nigh invulnerability, to rescue the wounded king. However, by that time, it is too late for Thorin to survive. After bearing the dying Thorin back to Dain's lines, Beorn is so overcome with rage on Thorin's behalf that he plunges right back into the fray. This time, when he comes to the bodyguard of Bolg, Beorn smashes right through it and kills Bolg himself, which marks a major turning point in the battle.
The cinematic reason is that Peter Jackson wanted to make a scene that does not exist in the book. In the book, Thorin is attempting to attack Bolg (replaced by Azog in the movie; in the book Azog actually died 150 years before the events of The Hobbit) when he is mortally wounded by Bolg's bodyguard spearmen before he reaches him. Beorn then smashes though the ranks and kills Bolg.
At the end of the battle, as Thorin lies dying, Gandalf brings Bilbo to him and Thorin dies with Bilbo, Gandalf and others there. As an aside in the book, Bilbo himself has a less then heroic battle; he is brave in his way but he gets knocked out by a rock and misses the battle (his ring means his body is not seen). In many ways this allowed Tolkien to skip over the majority of the battle, instead recounting only the bits that Bilbo has been told after he wakes up (remember The Hobbit is meant to be Bilbo's own account of his trip, written by him).
So Thorin has to die, but being one of the lead characters of 3 movies, Peter Jackson decided to give him and Bilbo very very different story endings. I mean, could you imagine it, Bilbo gets hit on the head, fade to black then wake up and it’s all over and Thorin dies being killed by Azogs henchmen as Azog watches and laughs before a giant bear eats him?
If you want a cinema story explanation, remember that the battle in the ruins between the 13 and the forces of Azog was happening away from the main battle front. Gandalf especially would have been in the middle of the main battle rallying the forces of elves, dwarves and humans. The whole point of the battle with Azog's forces was because the main army didn’t know an attack force was coming from there. By the time Bilbo had got to the main battle, sneaked or fought his way to someone who could help, then they had fought their way out of the battle to support them, the battle between the dwarves and the Orcs would have still been over.
As for one of the 4 you mention saving Thorin, magic is powerful but it can’t heal the kind of wounds Thorin was suffering from, it doesn’t magically knit flesh together or stop bleeding. Healing magic is more subtle and works to help the body heal naturally or fights poisons and infection. Thorin was bleeding out from a pretty big wound so even if Bilbo had got to one of the 4 and got them to Thorin (see point above for the trickery in that; remember there was still a battle going on!), by the time he explains what has happened, convinced them to go with him, and takes them to Thorin, Thorin will have died alone.