In command economies, someone needs to do the commanding. Unsurprisingly, the revolutionaries that install such systems often choose themselves for that role.
Yes, the Left is the ruling class. Or the establishment if you like.
Probably the idea that instead of class divide by wealth it would be class divide on political hierarchy (which would undoubtly divide on wealth as well)
I guess it's a reference to George Orwell's "All animals are equal, but some animals are more equal than others".
Maybe a reference to collectivization in Soviet Russia.