Is the ruler obligated to collect Zakat from Muslims, and how is its amount calculated, and how did the Rightly Guided Caliphs determine the amount of Zakat in a person's wealth?

The correct view is that the Muslim ruler must send out collectors to gather zakat (definition), based on the Almighty's saying: "Take, [O, Muhammad], from their wealth a charity by which you purify them and cause them increase," and based on the actions of the Prophet, peace and blessings be upon him, and his successors, and because some people are ignorant or avaricious. For apparent wealth, such as livestock and crops, reliance is placed on what is manifest. As for hidden wealth, such as gold, silver, and currency, reliance therein is placed on the owner's declaration.