good questions from lostepedia
I'll try to answer some of these questions.
What is the nature of the Island's time shifting phenomenon?
Where/when did the Island go?
I think I already answered that one.
What is seen by people not jumping in time when someone in front of them does?
Well so far according to the show it is only possible for people who are exposed to the particle cluster at the center of the Island (underneath the Orchid station) or the time barrier (which may be projected form this mass, which was previously located a short way off the coast and now and having changed position IE: decreased as a result of the move, and now effects all of the people on the Island.). In short, there has not been a scenario on the island where a person was susceptible to time travel among others who were not.
When Eloise (Daniel's lab rat) and Desmond were experiencing time travel, it appeared to the observer as if the trip and return were instantaneous, save for a few seconds of disorientation. When Desi traveled he was gone anywhere from seconds to days, but to Sayid it just seemed like he was "zoning out" and he asked "are you paying attention?" and Desmond quickly regained his senses and responded.
Why are Richard Alpert and the Others not affected by the time shifts?
I think it is because they have previously or are time traveling themselves, so they are on a different time vector as the Survivors and are not subject to the same circumstances.
Why is Juliet, a former member of the Others, affected?
Because she is a person that was brought to the Island, and she is not one of the original Others, such as Alpert, who where there before the Dharma Initiative.
Why does Daniel think the rules of time do not apply to Desmond?
Allready addressed.
Are the Flight 815 survivors who joined the Others affected or not? Why?
So far we haven't seen any of the Others besides Alpert, so we can't say what state they are in. It would be assumed that yes, they would be effected just the same as the other Survivors. Or it could be that they are in a place (the temple) that shields them from the time displacement properties.
What does the Beechcraft's crash tell us about where the Island might have physically moved to?
It tells us that the Island didn't move at all, because the plane crashed while the Island was in it's original location, or at least the one that the Survivors experienced prior to "moving it". If it was in a different physical location, then the plane could not have crashed there, because it wouldn't have been there for the plane to crash into.
Who is Daniel's mother and why does Desmond need to find her?
People have speculated that Mrs. Hawking is Daniel's mother, and obviously she has some special relationship with time travel.
Who are the soldiers that attack Sawyer and Juliet?
Why do they claim it is "their" Island?
They are probably members of the original Others. They looked to be WWII era and it could have been around the time that the radio broadcast tower was built and recorded the Numbers. Remember that Hurley's friend in the mental hospital overheard the transmission of the Numbers during the Korean war, which would have been before the Dharma Initiative.
Who are the assailants that attacked the beach camp with flaming arrows?
My guess is ancient inhabitants of the Island, from the time of the Black Rock's arrival or maybe even before when the Foot statue was built.
What does Ms. Hawking expect to happen in 70 hours?
For the Survivors to suffer death by cerebral hemorage that is the result of anyone who experiences what i have called the Time Displacement Factor. As we have seen it previously happen to Eloise, members of the Freighter crew, briefly Desmond, and now it's happening to Charlotte.
Why does Ben avoid Jack's question about Locke being dead and needing protection?
I'm not positive, but I think that it has to do with there being "two" Locke's from different times, one of them dead and the other one alive, as in the case of the rabbits and the Freighter doctor. And if it is indeed possible to change time, you can have him die in one time vector and saved from death to still live in another. Which is what i always predicted would happen after we first found out he was dead.
When the audience is told "they all must go back" why does this seemingly not include Walt?
My guess is because he wasn't on the Island when the Swan station imploded releasing the electro-magnetism. That is the only time travel connected phenomenon that he was excluded from compared to everyone else.