He went with Jack after the split because he doesn't like Locke
The long, underground tunnel in which Jeff, Michael, Locke, Hurley, and Charlie hid from the monster was a Cerberus Vent. Its circular, smooth edges would be ideal for the monster to travel through.
The apparitions of Savannah were, as Jeff believed, actually her way of contacting him from beyond death. Unlike most island apparitions, Savannah openly spoke with Jeff and even explained what had happened after he boarded the plane.