Vigor and how does milling actually work?

So I have questions dealing with Vigor being milled.

1. When I have to "mill 7", do i put the first 7 cards of my library in the graveyard at the same time or do I do them one after the other?

2. If it is the second thing, and I mill Vigor as my third card I shuffle it back in and then mill the other 4 cards or do I finish milling and only then does the Vigor reshuffle happen?

3. If it is the first option, i shuffle it back exactly the moment, is there a way to shortcut this in a more casual game? Like say I have ten cards left and mill 13. There is a chance I mill Vigor often enough that I have something left in my library afterwards. But I would need to physically shuffle each time, yes?