1. Who controls the world? Is there a global hierarchy?

The central bankers. They control the money, and money is power. They occupy the pinnacle of the global power structure.

2. And how does this covert control from the elites extend itself to areas such as our schools, media, economics, etc?

Through the "corporate-government partnership” ... i.e., modern fascism, which is of course a form of socialism. (That's why it is so amenable to communism, which is little more than fascism from a ground-level - or perhaps that should be "ditch-level" - perspective.).

3. And for what purpose is this mass social engineering and subjugation for?

To control / micromanage the world and its resources, including all of its “human resources”. Or in other words, to satisfy the cravings of a parasitic overclass addicted to money and power.