The item you have pictured will not come out intack. It's buried in the wall. To get it out in any condition will require you to damage the wall. If you sacrifice the wall to get the counter out, you have the issue of the metal pieces covering the laminate. You would need to remove all the metal pieces to relaminate. The metal pieces could not be reused as they would not fit anymore.
If the countertop wasn't buried in the wall, this would be job with decent results. You might be able to salvage the top itself, but the backsplash and the front wood trim will need to be replaced.
Did you ever finish this project from 2 years ago?
I'm asking because I just priced a prefab counter/backsplash Wilsonart brand (few inches too long, so I will cut the wall side). It's about $48. The end cap for exposed side is about $11, and the sidesplash for the wall side is about $18.
I figure $75 total, remove counter, replace counter, drop back in sink, not very expensive at all and easier to deal with than removing and replacing laminate sheets...