How Jacks dad was on the island? How his casket got there? How the cabin "dissapeared"? How walt showed up randomly? Possibly even Ekos brother's plane?

It seems that the effect of time jumping is not limited to people on the island, but also includes people NOT on the island, and possibly even inanimate objects.

I think we are jumping the gun here. The only proof of time travel we have seen is two of Desmonds flash backs. In both situations it was only his conscious that transfered between where he physically was in the future to where he physically was in the past. He had no control over location. Lets not confuse time travel with transportation. So I don't think this explains the disappearance and reappearance of characters like Christian and Walt. Remember, when Desmond travels, his body goes into a comatose state (it doesn't disappear).

How Jacks dad was on the island? How his casket got there? How the cabin "dissapeared"? How walt showed up randomly? Possibly even Ekos brother's plane?

It seems that the effect of time jumping is not limited to people on the island, but also includes people NOT on the island, and possibly even inanimate objects.
How about the polar bears?!
Orchid video anyone?!

Well is it truly time travel or a parallel universe. My theory right now is that the island must be a place where all these universes can collide. It's a kind of portal. I think this why the island is being hidden. Its a very dangerous place to cross into and out of. I think that may explain why one flight crashed with no survivors and another crashed with 48+ survivors.