Why the flashes of light, why the desert was the exit point and why they went back 30 years?

The following is an excerpt from Doctor Who: The Key to Time 2: The Destroyer of Delights.

Destroyer of Delights Link

The Guardian’s deep booming voice changes to a more normal tone and he admits that because the segments are already outside time, they’re also beyond his reach.

There’s a huge flash and the Doctor, Amy and the Guardian all find themselves literally flying through the air. The Guardian says he wants to show them something. He points to the River Nile below and tells them this is 9th century Sudan, the time of the Caliph al-Mutawakkil. Amy is getting a strange tingle, but it’s not like before and it’s not enough to suggest the next segment is anywhere close. The Guardian explains that he’s tried everywhere and there’s no trace of the segment being anywhere whatsoever. To illustrate the point he takes the Doctor and Amy to a location three miles beneath the crust of the planet Murphax VII where a volcanic eruption is imminent. The planet is orbiting the star of Perseus and if it wasn’t for the Guardian’s force field, the extreme heat would kill them. Amy feels as though the segment should be here, but she knows it isn’t.

The Guardian says that after a few more millennia he stumbled across the planet Alpha III. He takes them to a dead forest which will soon find itself under a mile of ice for ten thousand years. Amy still can’t sense any of the segments, but the Guardian says that in all the time he was searching, these locations were the prime candidates. He admits defeat and says he can’t offer any advice as to where the segments could be. They could be disguised as anything - a grain of sand, a leopard’s tooth, a blob of molten lava or even an atom of snot. He searched throughout time and can’t find them. They’re out of options and if they fail in their mission, it’ll mean the end of time.

The Doctor suggests they try something completely at random. He says the Guardian has been absolutely methodical in his methods, so the only thing left to do is to search in a manner that’s heedless of any sense and dictated only by chaos. It requires a leap of faith, so the Guardian agrees to let them find their own destination and says he’ll track them down and join them once they’ve gone. He can already feel the onset of entropy, so every second counts. He uses the last of his power to send the Doctor and Amy on their way, with no idea where they will end up…

The Doctor comes crashing to earth and finds himself in the middle of a desert. Amy is nowhere to be seen. His arrival has been seen by a group of men from a nearby camel caravan and they immediately mistake him for a bandit. The leader of the men, Hasan, mounts his camel and charges towards his prey with his lance raised, ready to kill the bandit. The Doctor insists that he‘s merely a lost traveller, but the men don‘t believe him and are convinced he has criminal brethren waiting nearby. When it becomes clear that the Doctor isn’t even armed and appears to have just fallen out of the sky, the men back down, but Hasan remains cautious and grants him permission to continue living as his slave. When the Doctor tries to explain how he got there, Hasan mistakes him for a story-teller and assumes he’s heading for the city of Dunqulah.

I have highlighted the points that are important.  First The Guardian’s deep booming voice changes to a more normal tone and he admits that because the segments are already outside time, they’re also beyond his reach.  This is Smokey starting his loophole.  At this point in the story he can't touch the candidates and he sets about his plan to eliminate them.  He tell John Locke, in the cabin, he has to move the island. 

"There’s a huge flash".  In Doctor Who the Black Guardian was showing them where he had searched for the remaining keys to time without success throughout time.  This is the reason why in Lost that everytime they go to a different point in time there is a bright flash of light.

The Doctor suggests they try something completely at random. He says the Guardian has been absolutely methodical in his methods, so the only thing left to do is to search in a manner that’s heedless of any sense and dictated only by chaos.  This is the reason why they jump through time in a random pattern.

They’re out of options and if they fail in their mission, it’ll mean the end of time.   You know if you are a Lost fan that if Smokey got off the island it means that everything will end. 

Remember this statmement:  Widmore’s statement to Jin Kwon said the following:  If that thing masquerading as John Locke ever got off this island your wife, your daughter, my daughter everyone we know and love would simply cease to be.

It requires a leap of faith.  This refers to Jack now having to become a man of faith and it is only fitting that this transformation takes place in a church where Ben is telling him the bible story about "Doubting" Thomas.

The Doctor comes crashing to earth and finds himself in the middle of a desert.  The desert in Tunisia was the
 exit point from the island once the wheel was turned.
  

Now onto why the 30 year jump in time.  We know that 3 years had passed since the Oceanic 6 had left the island which makes it 2007.  When Jack and crew made it back to the island they were now in 1977.  But why?

The following is an excerpt from Doctor Who: The Key to Time 2: The Judgement of Isskar.

The Judgement of Isskar link

For 12,000 years, life on Mars prospered peacefully. It was a world of builders, craftsmen and farmers - until the day the ground and sky betrayed them. When the plug was pulled from the gravity well it sent earthquakes and hurricanes across the planet surface for three decades. Almost everything was lost. A few managed to get off the world, but the rest fought amongst themselves for food and shelter. After 30 years the energies were spent and the ground settled down.

They went back 30 years from the two highlighted quotes above.  Remember when it was all said and done and what Miles said afterwards:

[Topside, Jin, Miles, Juliet, and Sawyer stand about, and the earth begins to shake. Flashes shoot at them and they grab their heads. And fall to the ground, kneeling, as a buzzing and magnetic humming overtakes all other sound. Down below, a look of surprise comes over Locke's face. Up above, the group is totally overcome by the rapid-fire flashes, and they all fall to the ground. White light envelopes everything, and the buzzing and humming stop. Miles holds his head, panting on the ground. Sawyer lifts himself up.]

JULIET: What the hell was that?

MILES: [Panting] That one was different. It was... that was more like an earthquake.

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