How do I enable the livemap to show changes done on the server? I mean terrain that has been changed, say a new clay spot is made or a player flattens a 60x60 spot, etc. The servers I have played on the livemap shows these changes, on my server it does not. Read documentation for livemap and tools in the livemap and I don't see an option for this.

There is no built-in function for such tracking.
The Livemap is open-source. Everyone can modify it or add to it at their own discretion.