As others have said, a creature affected by a power knows exactly what effects are on it. The example for divine challenge says that the creature knows it is marked and will take damage if it attacks anyone other than the paladin - thus, the creature knows the game effects, including the identity of other specific creatures connected to them, but I don't see that it knows the name, class or level of the power, or who or what caused it, unless it can guess from the visual display or game effects. edit: It knows the power source for the effect because that's a keyword of every power. It doesn't learn your location.
Warlock's curse lasts until the end of the encounter or until the cursed target drops to 0 hit points, as it says in the description.
What source of invisibility? Read the description of that power. Presumably it isn't eyebite because the creature isn't aware of the warlock's presence. If the warlock had invisibility, Wizard Utility 6, cast on him by the party's wizard, he becomes visible if he attacks, as you mentioned. Warlock's curse doesn't require an attack roll, has no immediate effect on the target, is not one of the four types of attacks listed on page 56 and is not an attack power - note that I'm not saying that any of these are the definition of an attack, but together they suggest to me that warlock's curse is not an attack. (It would be really helpful if Attack was a keyword.)