If I have a Duplicant on the top of my 'yard and I cast a Volrath's Shapeshifter, can the VS imprint a creature in play?
Yes. It will come into play and will get Duplicant's text. Its Imprint abiltiy will trigger and you can remove a creature.
If so, what happens when the Volrath's Shapeshifter ceases being a Duplicant (I'm assuming it would still have the creature imprinted on it, even though it would no longer be a Duplicant)? Does it still have the power and toughness of the creature imprinted on it?
It still has the creature imprinted on it. It no longer has that creature's power and toughness or creature types since it no longer has the Static ability that creates that effect.
What happens if it becomes a Duplicant again at a later time? Would it have the power and toughness of the creature imprinted on it? Or would it need to imprint another creature?
It would have the power and toughness of the imprinted creature. If you manage to get multiple creatures imprinted on it, it will have the power and toughnesss of the last creature card imprinted on it.
Note the Oracle text, which was changed to fix certain interactions with VS.
Duplicant
6
Artifact Creature - Shapeshifter
2/4
Imprint - When Duplicant comes into play, you may remove target nontoken creature from the game. (The removed card is imprinted on this artifact.)
As long as a creature card is imprinted on Duplicant, Duplicant has the power, toughness, and creature types of the last creature card imprinted on it. It's still a Shapeshifter.