Answer: Man in Locke says that the people whose names are on the cave were pushed and manipulated by Jacob to get them to the island (Ep: 6x4, The Substitute). Jacob gave Ilana a list of the six remaining candidates for her to protect (Ep: 6x9, Ab Aeterno). It appears that the chosen candidate needs to keep Man in Black on the island so that evil cannot spread throughout the world.
Jacob tells Sawyer, Kate, Jack, and Hurley that he brought them to the island as possible protectors of the island because they were flawed and they needed the island as much as the island needed them (Ep: 6x16, What They Died For).
After Juliet detonated the bomb, our characters returned to the 2007 timeline. In the flash-sideways in 2004, we saw that the island was underwater. What happened to Man in Black and Jacob?
Answer: I am now convinced that the bomb never detonated (it would have destroyed the island). I think the flash to white was the Losties returning to 2007. Later, when Juliet told Sawyer, "It worked," she was dying and moving back and forth between the island and the flash-sideways. When she was thinking "It worked," she was talking about the vending machine.
The island was going to be underwater, but that was changed when Kate killed Man in Locke. Or, the island was under water way in the future.
Jack mentions him a couple of times in the future as if he is alive. If he's not alive, how is he seen on the island?
Answer: According to Man in Locke, he was posing as Christian Shephard on the island (Ep: 6x13, The Last Recruit). But that begs the question, who was posing as Christian Shephard when Jack saw him off the island?
Was it Jacob? Was it Black Shirt pretending to be Jacob?
Answer: We really don't have a definitive answer to this one, but we've got a good discussion going: What's the story with the cabin?
Answer: We still don't know who built it, but it was destroyed in 1867 when the Black Rock smashed through it when the ship crashed on the island (Ep: 6x9, Ab Aeterno).
16. Who's Coming?
And how do they leave the island?
Answer: It appears that Jacob stopped aging when Mother gave him some liquid to drink in front of the light cave (Ep: 6x15, Across the Sea).
Richard doesn't age because Jacob made him ageless after he came to the island in 1867. Richard was sent by Man in Black to kill Jacob, but Jacob explained that Man in Black was evil. Jacob asked Richard to help him with the people he brings to the island and gave Richard eternal life in exchange for his help (Ep: 6x9, Ab Aeterno).
Answer: The ankh from the four-toed statue. Hurley took the case to the Temple and Dogen opened it, took out the ankh, broke it, and pulled a piece of paper from it. (Ep: 6x2, LA X Part 2)