Keeping Perfect Time Forever

I am having a difficult time wrapping my head around the Space-Time Crystal, a four-dimensional device proposed by scientists at the Berkeley Lab.  This four-dimensional crystal has periodic structure in both space and time, and could be used to build a clock that would keep perfect time, even after the heat-death of the universe.

I do have some questions:
1.  Where will this device reside once the universe is gone?
2.  What is the point of keeping time after everything is gone?
3.  Is there an assumption that there will be another big-bang after the death of the universe and the device will then be in the new universe?
4.  If the assumption in the previous question holds true, since we measure time in a very earthly manner, what will it mean to the beings that get into the possession of this device?

Anyone care to elaborate?