The way it was filmed was ambiguous, so I'm not surprised that there was confusion.

Jae = bald dude who had affair with Sun, died on Jin's car.

Died on Jin's car, or midair due to heart attack? The conspiracy continues...

I don't think Ben was conning Sawyer at all

The Hydra Station and therefore where Jack, Sawyer, and Kate are being held, is definitely on a separate island than the rest of the 815 survivors. The Hydra station wasn't on Kelvin's black light map.

True. However, the map does have a notation for "Subterranean Conduit", which might be how, as some have theorized, the Others can move from the Hydra to the main island.