Regarding the island moving through time and space:
Damon and Carlton have confirmed that the island does move through both when the Frozen Donkey Wheel is turned in a past PodCast episode. Regarding Jack recognizing Desmond during the flash-sideways:
On the PodCast for this episode, Damon teases us about that moment. He mentions the possibility that Jack barely remembers Desmond from their first meeting in the stadium. Yet, he also teases that perhaps there’s something more cosmic at work; their timeline might never had Jack and Desmond meet. If that’s the case, Jack would have no reason to recognize Desmond, and would suggest there’s some residual memory or injection of the original timeline. So, that’s up in the air for now, by design.
Official prediction: LA X timeline will involve Island survivors interacting with the Lostees and embroiling them, perhaps even by sheer accident, in efforts to fix whatever went wrong with the Island. The success of this effort will both restore the original timeline as well as explain why THESE people are so important to it.