a) The rate of fire is unpossible with his Manlicher Carcano .
I don't know why this always comes up. How long do you think it takes for a well trained person to cycle a round? It's less than a second. It would not be hard at all for trained marksmen (which he was) to shoot three times and hit the target twice at that very short range.
History had a show about that a few years ago. Trained marksmen was able to get off that many shots and hit a moving target at that distance, get out of the building and get to where he was when he was found.
People love conspiracy theories, even when actual facts don't line up.