Are they all just cool with a king that acts like this
It obvious that those that thrive in the Palace environment are sadists themselves and so are able to indulge their perverse inclinations in that place. They, at least, would be fine with this sort of King. I suspect, though, what happens in the Palace generally remains in the Palace as the ML seems surprised at what he is discovering.
The story lets us know that the King pretty much murdered his way to the throne. I would guess that the rest, especially outside of the Palace, that do have any idea of the real picture, turn their heads, keep a low profile (as our ML hoped to be able to do) to avoid bringing that bloody attention on themselves.