Court of Vantress

Any enters-the-battlefield abilities of the copied permanent will trigger when the token enters the battlefield. Any "as [this permanent] enters the battlefield" or "[this permanent] enters the battlefield with" abilities of the permanent will also work.

When Court of Vantress becomes a copy of a permanent, it's neither entering nor leaving the battlefield. Any enters-the-battlefield or leaves-the-battlefield abilities won't trigger.

The game starts with no monarch. As a player becomes the monarch, the current monarch (if any) ceases being the monarch. There is never more than one monarch at a time.

The token copies exactly what was printed on the original permanent and nothing else (unless that permanent is itself copying something else; see below). It doesn't copy whether that permanent is tapped or untapped, whether it has any counters on it or Auras attached to it, or any non-copy effects that have changed its power, toughness, types, color, and so on.

If the monarch leaves the game during another player's turn, that player becomes the monarch. If the monarch leaves the game during their turn, the next player in turn order becomes the monarch.

There are two inherent triggered abilities associated with being the monarch. These triggered abilities have no source and are controlled by the player who was the monarch at the time the abilities triggered. The full texts of these abilities are "At the beginning of the monarch's end step, that player draws a card" and "Whenever a creature deals combat damage to the monarch, its controller becomes the monarch."