Do factions exist within the top level of any regime? Why?

To put it simply, most people in the top levels of any regime are by nature ambitious, they can't all be president. There's also differences on the best way to go about things.

You do realize that a leader picks people he wants around him. Usually people with the same opinions and outlook on life.

The leader isn't always in that position. Hitler despised Goering but he made him his deputy.