Haha trueWe don't know.
We might find out in the follow up series though. All we do know is that he didn't have it in The Last, although he was travelling the world and only popped back to the village to drop Hiashi off and have a boss moment.
Not like he needs it.
No, he didn't and he probably never will. It was his choice to have it this way.
He probably sees it as a punishment. It was also his main arm, the one he used his chidori with all the time. The one he tried to kill his friends with.