Do I get to keep the 2nd Kalonian Twingrove when I got it via a Mimic Vat?
The rulings on Mimic Vat say: 


  Any enters-the-battlefield abilities of the exiled card will trigger when the token is put onto the battlefield. Any "as [this permanent] enters the battlefield" or "[this permanent] enters the battlefield with" abilities of the exiled card will also work.


This means that you will get one token copy of a Kalonian Twingrove, and one Treefolk Warrior token. The Treefolk Warrior token won't be exiled, as it wasn't created by the Mimic Vat.

This is assuming you have any forests in play. If you do not, then both tokens will immediately die for having 0 toughness and vanish!