Light falls off with distance, so (all other things being equal) I'd guess no.
I'd think if you were to be able to somehow move a person's head in a perfectly straight line, starting from across the room to 2 feet away from the diamond the amount of sparkle would not change, though the apparent size of the sparkles would increase.
depends on the lighting and angles as well as the cut.
The answer in my opinion is around 15 inches.
Far enough away that obstruction is reduced but close enough to get a lot of light return to the eye and allow light coming from around your head to strike the diamond.
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