Can a goalkeeper use his hands if he is in the offesive zone?

Not in the other goalkeeper's penalty area, only in his own. It would be a handball if he'd done so.

Goalkeepers cant use hands except if there in there box, if they come out the same rules that apply to outfield players apply to the goalkeeper, if not the keeper could pick up the ball and run straight for the net. I wonder if thats how rugby started?

NO. Once a goalie comes out of his penalty area he is just like any other player. If he handles the ball he could get a red card.

Absolutely the goal keeper cant punch the ball outside his defensive zone

No they only can use their hands in their own box or else they would have the goalie run down the field with the ball in their hands.

No, he was not allowed to use his hands within the opponent's penalty area. You'll notice he did not actually use them.

yes

no he could not silly bollocks