The River/WMG

"The Source" is The Heart of the Island.
In the episode where "The Source" is revealed, the Magus will be consumed by bright white lights on their way toward it. The boat will tip over, and the Cole-family (they've probably found the Emmet by this point,) plus Lena get out of the boat, finding themselves in the middle of a bamboo jungle. After some walking around, being unknowingly tracked by Kurt Brynildson (who is (or was) on Charles Widmore's team), they find a River (the titular one, leading towards a double-meaning) leading into a cave full of light - "the Source" they've been looking for. Don't know when this is set within the LOST-universe in terms of chronology though - perhaps Hurley's Candidates? Anyway, ABC owns both show so it could be.

Lincoln is
We already know that Tess  but not how long it was going on or when it was really found out. Lincoln also mentions how at some point his father stopped acting like he was the center of his world. There are a few different reasons of why this could be, but finding out Lincoln isn't his son could be it.
 * Jossed. Tess.

AJ has a boyfriend back home.
When he was underneath the tree and thinking he was about to die, AJ mentioned that he loved a "David." Maybe that's his boyfriend.
 * Confirmed. Good call.