That's not Vettel's advantage. Hamilton had a chance to pass Vettel on the other side and even if Hamilton didn't pass, he was then right under Vettel's rear-wing instead of 1.0-1.5s back before the incident, and on top of that Vettel would have temperarily dirty tyres. All of that is advantage Hamilton. The gap between Vettel and Hamilton went from 1.0 or 1.5 seconds to basically 0.1 seconds, that's advantage Hamilton.
Yup. He was most definitely modulating or holding throttle, not even close to full throttle or he would have been spinning up the tyres like crazy along with his revs skyrocketing. He was just trying to manage and hold the car steady the entire time.
Vettel went across the track, how could Hamilton pass on the left? If the track was a 'normal' track, without walls then Hamilton was passed, or at least have the inside for the next corner - advantage Vettel. The reduction of the gap was due to Vettels mistake, its not an unfair advantage for Hamilton.