I think whatever is going on with Sinestro is certainly related back to Hal and his dad and grandfather. Maybe he was giving himself another chance to save Sinestro from himself because he could not save his dad from himself.
As for the ring: Hal made a big point about how John could hold onto a projection even when he was not wearing the ring; that that was something no other Lantern could do. Maybe Hal, or more specifically, Hal-o-gram, also has one last thing that only he can do. I mean this is probably wrong but I will hold out hope until next week that it is right: that when the chips are down and the ring is out of juice and Hal-o-gram is fading away while "the threat" looms that that is when he says the oath like we heard it in the trailer: "In brightest day, in blackest night, No evil shall escape my sight. Let those who worship evil's might, Beware my power - Green Lantern's light!" and something about Hal being Hal and Hal-o-gram being a creature of the ring allows it to connect directly to the Central Battery and recharge while Hal fades away for the last time leaving John with a fully powered ring.