Please help me understand - if civil marriage took place in Panama, was registered in panama'; the divorce took place in the U.S.A, what makes the divorce legal in Panama'. Does the divorce needs to be registed in Panama?

First its not a good idea to piggyback your question on another thread. This can lead to confusion. So I've moved your question to its own thread.

Most countries have reciprocal treaties where civil actions like marriages and divorces are recognized by each other.

The divorce is legal there the same way the marriage is legal in the US. They are just honored by the other nations.