This is partially covered on page 26 of the DMG:
"Gotcha!" Abilities: Pay attention to monster abilities that change the basic rules and tactics of combat and give players the cues they need to recognize them. Describe the ability as it might appear in the game world, and then describe it in game terms to make it clear.
For example, if the characters are fighting a pit fiend, whose aura of fire deals fire damage to creatures within 5 squares, you might tell the players (before their characters come in range), "The heat emanating from the devil is intense even at this distance. You know that getting within five square of it is going to burn you."
So in the case of your example, yes, the players should be informed about the aura. They should also probably be informed of particularly unusual reactions/opportunity actions. They probably don't need a blow-by-blow rundown of every power the creature has, however... That's what knowledge checks are for.
For example, the fighter player-character class has the ability to make an opportunity attack whenever someone marked by it shifts. I would tell player characters (and allow monsters to know) about this ability at the time one of them is marked.