How was the Man in Black able to appear as Christian Shephard to Jack off the Island?
Since the Man in Black wasn't able to leave the island, it is likely that Jack's off-Island visions of his father were psychological, due either to substance abuse or simply stress. ("Something Nice Back Home")
Jacob's intent for the Others was, with the help of Richard, was to use The Others as intermediaries between him and the people whom he brought to the island. He did not want to get involved with their actions because he wanted to prove that people could be good on their own accord, so he used the Others to communicate with the people. Their primary goal was to protect the island from the Man in Black and other threats, specifically protecting The Source. ("Solitary") ("Ab Aeterno")
Why did they kidnap children?
The Others kidnapped children to supplement their population and experiment because they were unable to give birth to babies on the island. ("Raised By Another") ("Not in Portland")
Each number corresponds to the degree Jacob must turn his wheel to view candidates in the lighthouse. Each number was the degree of the remaining 6 candidates for his replacement. They were a sort of filing system, as seen in his cave. ("The Substitute") ("Lighthouse")
Why did reappear regularly both on and off the Island?
The Numbers also represent the factors of the core values of the Valenzetti Equation, which predicts the date of the destruction of mankind. These Numbers correspond somehow to various human and environmental factors, likely meaning that they are somehow embedded in the structure of the universe. This is also likely why the Numbers appeared to be cursed. The purpose of the DHARMA Initiative was to alter these values in order to stave off the destruction of mankind. The values were broadcast from the radio tower, with the intent of using the broadcast to determine when DHARMA had succeeded in changed them. ("The Lost Experience")
Why were they wearing priest outfits, even though the plane was filled with Virgin Mary statues filled with heroin, and one of the corpses has a gun?
Because Yemi, the corpse found by Boone on the plane was an actual Catholic priest, whose help the drug smugglers (Eko, Olu and "Goldie") needed as only foreign and missionary planes were allowed to take off from Nigeria. He helped them, after they threated to burn down his church. ("The 23rd Psalm")
How was a plane which took off from Nigeria crash on an island which is supposedly in the Pacific?
What are the pregnancy issues experienced on the Island?
Women who get pregnant on the Island are not able to bear their children to term. Sometime before the third trimester, the women experience a serious miscarriage which results in the deaths of both the child and the mother. Women who conceive off Island, such as Claire seem to be able to give birth without issue, as well as women such as Sun who leave the Island before their third trimester. ("Do No Harm") ("Not In Portland") ("D.O.C.") ("Ji Yeon")
Were women ever able to give birth on the Island?
Yes. As late as the 1970s, women were able to carry a child to term on the Island, as seen by Amy's delivery of Ethan. ("LaFleur")
What does the Island do to the reproductive systems of its inhabitants?
Something on the Island causes the uterus of women on the Island to age and deteriorate rapidly. Men, on the other hand, experience a five-fold increase in their sperm counts while on the Island, possibly due to the healing properties of the Island. ("Not in Portland") ("D.O.C.")
What caused women to be unable to bear children on the Island?
They discovered the Wheel while digging to the Source. Since Dr. Chang stated that they did initially plan to use the electromagnetic energy to time travel, they most likely studied the wheel to determine how to use the energy to accomplish it. ("Because You Left")
How was the wheel accessed and installed as it predated the DHARMA station?
They were dug because the Man in Black wanted to reach the Source and use it as a way to escape the Island. ("Across the Sea") They were dug on top of energy pockets where the Man in Black and his friends were lead by their compasses. ("The Last Recruit")
The Source is the electromagnetic core of the island. The electromagnetism found deep within the island originates here and radiates out to other parts of the island, so therefore it exists here in its most powerful form. ("The End")
Why must it be protected?
The Source must be protected because if the energy is released, it could cause a global catastrophe. Similar to the Swan Incident, the electromagnetic expulsion caused the island to shake, but much more severely. Cliffs began to split in half and there were landslides and rockfalls. If it had escalated, the implications could have been disastrous. ("The End")