Alright, here's my deduction: The short, fat one with glasses isn't their brother at all. He must have faked the hand injury by burning it himself after comparing with the oldest brother's injury.
My reasoning for that is that he said the pot was quite hot when they all grabbed it, but he was the only one who mentioned temperature.
He was also the only one who didn't mention receiving a gift from him.
He also looked at the second son after being asked who got there first. If he was the last one, how could he have known which one of the two were the first?
Maybe the reason one of the lenses is broken is because the fatso was wearing those glasses, got into a fight and got the lens broken, then after the death switched up the glasses to not cause suspicion.
But now we'll have to wait one month to know if I'm right or not.