Are you equating Fiqh-e-Hanfia with some sort of political system? The excerpt says that the head of the state of the time (how will he be elected, that is another point you are yet to clarify) decided to bestow official recognition upon a legal system devised by an individual heading a council of jurists. It does not answer a single one of my questions. How is that council of jurists formed? How are its members elected? How is the head of the council decided? What is the mechanism of the head of the state adopting the laws of a council? Nothing on any of this.

The second link talks about the international law devised by Muslims in the 8th century and its influence on the future lawmakers of the world. Without answering my questions, it raises further issues. Is the international law devised in the 8th century (when the concept of nationhood, international organizations, treaties, and scores of other factors peculiar to the modern world did not exist) to be implemented in the 21st century?

That is beside the point. First you have to clarify what is the Islamic way of electing the members of the other two houses (if two houses is what Islam prescribes. Does it?).