The Power Nap should be there in the next Kai episode. It's the reason why Vegeta is not present during the Porunga summoning scene and why Kuririn and Gohan get away with two wishes behind his back. I remember him falling asleep while holding a strange device which might've been what supposely increased his power. I guess we'll see next episode. It does sound too dumb to be true, but it's how I remember it.
And about his 3rd power up: